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@article{Pezze2017,
abstract = {A quantum theory of multiphase estimation is crucial for quantum-enhanced sensing and imaging and may link quantum metrology to more complex quantum computation and communication protocols. In this letter we tackle one of the key difficulties of multiphase estimation: obtaining a measurement which saturates the fundamental sensitivity bounds. We derive necessary and sufficient conditions for projective measurements acting on pure states to saturate the maximal theoretical bound on precision given by the quantum Fisher information matrix. We apply our theory to the specific example of interferometric phase estimation using photon number measurements, a convenient choice in the laboratory. Our results thus introduce concepts and methods relevant to the future theoretical and experimental development of multiparameter estimation.},
author = {Pezz{\`{e}}, Luca and Ciampini, Mario A. and Spagnolo, Nicol{\`{o}} and Humphreys, Peter C. and Datta, Animesh and Walmsley, Ian A. and Barbieri, Marco and Sciarrino, Fabio and Smerzi, Augusto},
doi = {10.1103/PhysRevLett.119.130504},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Pezz{\`{e}} et al. - 2017 - Optimal Measurements for Simultaneous Quantum Estimation of Multiple Phases.pdf:pdf},
issn = {10797114},
journal = {Physical Review Letters},
number = {13},
pages = {130504},
title = {{Optimal measurements for simultaneous quantum estimation of multiple phases}},
volume = {119},
year = {2017}
}
@inproceedings{Zhang2016FiO,
address = {Rochester, NY},
author = {Zhang, Lu and Chan, Kam Wai Clifford and Verma, Pramode K},
booktitle = {Frontiers in Optics/Laser Science (FiO/LS)},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Zhang et al. - 2016 - Quantum Multiple Phase Estimation Using Balanced Multi-mode Entangled States.pdf:pdf},
pages = {Paper JW4A.194},
title = {{Quantum multiple phase estimation using balanced multi-mode entangled states}},
year = {2016}
}
@article{Schrodinger1935,
abstract = {ABSTRACT The probability relations which can occur between two separated$\backslash$nphysical systems are discussed, on the assumption that their state$\backslash$nis known by a representative in common. The two families of observables,$\backslash$nrelating to the first and to the second system respectively, are$\backslash$nlinked by at least one match between two definite members, one of$\backslash$neither family. The word match is short for stating that the values$\backslash$nof the two observables in question determine each other uniquely$\backslash$nand therefore (since the actual labelling is irrelevant) can be taken$\backslash$nto be equal. In general there is but one match, but there can be$\backslash$nmore. If, in addition to the first match, there is a second one between$\backslash$ncanonical conjugates of the first mates, then there are infinitely$\backslash$nmany matches, every function of the first canonical pair matching$\backslash$nwith the same function of the second canonical pair. Thus there is$\backslash$na complete one-to-one correspondence between those two branches (of$\backslash$nthe two families of observables) which relate to the two degrees$\backslash$nof freedom in question. If there are no others, the one-to-one correspondence$\backslash$npersists as time advances, but the observables of the first system$\backslash$n(say) change their mates in the way that the latter, i.e. the observables$\backslash$nof the second system, undergo a certain continuous contact-transformation.$\backslash$n},
author = {Schr{\"{o}}dinger, E.},
doi = {10.1017/S0305004100013554},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Schr{\"{o}}dinger - 1935 - Discussion of probability relations between separated systems.pdf:pdf},
isbn = {1469-8064},
issn = {14698064},
journal = {Mathematical Proceedings of the Cambridge Philosophical Society},
number = {4},
pages = {555--563},
title = {{Discussion of probability relations between separated systems}},
volume = {31},
year = {1935}
}
@article{Rozema2014,
author = {Rozema, Lee A and Bateman, James D and Mahler, Dylan H and Okamoto, Ryo and Feizpour, Amir and Hayat, Alex and Steinberg, Aephraim M},
doi = {10.1103/PhysRevLett.112.223602},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Rozema et al. - 2014 - Scalable Spatial Superresolution Using Entangled Photons.pdf:pdf},
journal = {Physical Review Letters},
number = {22},
pages = {223602},
title = {{Scalable spatial superresolution using entangled photons}},
volume = {112},
year = {2014}
}
@article{Calkins2013,
abstract = {The integrated optical circuit is a promising architecture for the realization of complex quantum optical states and information networks. One element that is required for many of these applications is a high-efficiency photon detector capable of photon-number discrimination. We present an integrated photonic system in the telecom band at 1550 nm based on UV-written silica-on-silicon waveguides and modified transition-edge sensors capable of number resolution and over 40{\%} efficiency. Exploiting the mode transmission failure of these devices, we multiplex three detectors in series to demonstrate a combined 79{\%} +/- 2{\%} detection efficiency with a single pass, and 88{\%} +/- 3{\%} at the operating wavelength of an on-chip terminal reflection grating. Furthermore, our optical measurements clearly demonstrate no significant unexplained loss in this system due to scattering or reflections. This waveguide and detector design therefore allows the placement of number-resolving single-photon detectors of predictable efficiency at arbitrary locations within a photonic circuit - a capability that offers great potential for many quantum optical applications.},
author = {Calkins, Brice and Mennea, Paolo L. and Lita, Adriana E. and Metcalf, Benjamin J. and Kolthammer, W. Steven and Lamas-Linares, Antia and Spring, Justin B. and Humphreys, Peter C. and Mirin, Richard P. and Gates, James C. and Smith, Peter G. R. and Walmsley, Ian A. and Gerrits, Thomas and Nam, Sae Woo},
doi = {10.1364/OE.21.022657},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Calkins et al. - 2013 - High quantum-efficiency photon-number-resolving detector for photonic on-chip information processing.pdf:pdf},
isbn = {9781557529725},
issn = {1094-4087},
journal = {Optics Express},
number = {19},
pages = {22657--22670},
pmid = {24104153},
title = {{High quantum-efficiency photon-number-resolving detector for photonic on-chip information processing}},
volume = {21},
year = {2013}
}
@article{Yue2014,
abstract = {We present a general quantum metrology framework to study the simultaneous estimation of multiple phases in the presence of noise as a discretized model for phase imaging. This approach can lead to nontrivial bounds of the precision for multiphase estimation. Our results show that simultaneous estimation (SE) of multiple phases is always better than individual estimation (IE) of each phase even in noisy environment. The utility of the bounds of multiple phase estimation for photon loss channels is exemplified explicitly. When noise is low, those bounds possess the Heisenberg scale showing quantum-enhanced precision with the O(d) advantage for SE, where d is the number of phases. However, this O(d) advantage of SE scheme in the variance of the estimation may disappear asymptotically when photon loss becomes significant and then only a constant advantage over that of IE scheme demonstrates. Potential application of those results is presented.},
author = {Yue, Jie Dong and Zhang, Yu Ran and Fan, Heng},
doi = {10.1038/srep05933},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Yue, Zhang, Fan - 2014 - Quantum-enhanced metrology for multiple phase estimation with noise.pdf:pdf},
issn = {20452322},
journal = {Scientific Reports},
pages = {5933},
pmid = {25090445},
title = {{Quantum-enhanced metrology for multiple phase estimation with noise}},
volume = {4},
year = {2014}
}
@article{Kok2002,
abstract = {Large photon-number path entanglement is an important resource for enhanced precision measurements and quantum imaging. We present a general constructive protocol to create any large photon number path-entangled state based on the conditional detection of single photons. The influence of imperfect detectors is considered and an asymptotic scaling law is derived.},
author = {Kok, Pieter and Lee, Hwang and Dowling, Jonathan P.},
doi = {10.1103/PhysRevA.65.052104},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Kok, Lee, Dowling - 2002 - Creation of large-photon-number path entanglement conditioned on photodetection(2).pdf:pdf},
isbn = {1050-2947$\backslash$n1094-1622},
issn = {10941622},
journal = {Physical Review A},
number = {5},
pages = {052104},
title = {{Creation of large-photon-number path entanglement conditioned on photodetection}},
volume = {65},
year = {2002}
}
@article{Mullin2011,
abstract = {NOON states (states of the form {\$}|N{\textgreater}{\_}{\{}a{\}}|0{\textgreater}{\_}{\{}b{\}}+|0{\textgreater}{\_}{\{}a{\}}|N{\textgreater}{\_}{\{}b{\}}{\$} where {\$}a{\$} and {\$}b{\$} are single particle states) have been used for predicting violations of hidden-variable theories (Greenberger-Horne-Zeilinger violations) and are valuable in metrology for precision measurements of phase at the Heisenberg limit. We show theoretically how the use of two Fock state/Bose-Einstein condensates as sources in a modified Mach Zender interferometer can lead to the creation of the NOON state in which {\$}a{\$} and {\$}b{\$} refer to arms of the interferometer and {\$}N{\$} is the total number of particles in the two condensates. The modification of the interferometer involves making conditional ``side'' measurements of a few particles near the sources. These measurements put the remaining particles in a superposition of two phase states, which are converted into NOON states by a beam splitter. The result is equivalent to the quantum experiment in which a large molecule passes through two slits. The NOON states are combined in a final beam splitter and show interference. Attempts to detect through which ``slit'' the condensates passed destroys the interference.},
author = {Mullin, W. J. and Lalo{\"{e}}, F.},
doi = {10.1007/s10909-010-0234-z},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Wolfgramm, Cer{\`{e}}, Mitchell - 2002 - Generation of three-photon entangled state by quantum interference between a coherent state and pa(4).pdf:pdf},
issn = {00222291},
journal = {Journal of Low Temperature Physics},
number = {3-4},
pages = {250--257},
title = {{Creation of NOON states by double Fock-state/Bose-Einstein condensates}},
volume = {162},
year = {2011}
}
@article{Wolfgramm2010,
abstract = {Indistinguishable photons play a key role in quantum optical information technologies. We characterize the output of an ultra-bright photon-pair source using multi-particle tomography [R. B. A. Adamson et al., Phys. Rev. Lett. 98, 043601 (2007)] and separately identify coherent errors, decoherence, and distinguishability. We demonstrate generation of high-quality indistinguishable pairs and polarization NOON states with 99{\%} fidelity to an ideal NOON state. Using a NOON state we perform a super-resolving angular measurement with 90{\%} visibility.},
author = {Wolfgramm, Florian and Cere, Alessandro and Mitchell, Morgan W.},
doi = {10.1364/JOSAB.27.000A25},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Wolfgramm, Cere, Mitchell - 2010 - NOON states from cavity-enhanced down-conversion high quality and super-resolution.pdf:pdf},
issn = {0740-3224},
journal = {Journal of the Optical Society of America B},
number = {6},
pages = {A25--A29},
title = {{NOON states from cavity-enhanced down-conversion: high quality and super-resolution}},
volume = {27},
year = {2010}
}
@article{Somaschi2016,
abstract = {Single-photons are key elements of many future quantum technologies, be it for the realisation of large-scale quantum communication networks for quantum simulation of chemical and physical processes or for connecting quantum memories in a quantum computer. Scaling quantum technologies will thus require efficient, on-demand, sources of highly indistinguishable single-photons. Semiconductor quantum dots inserted in photonic structures are ultrabright single photon sources, but the photon indistinguishability is limited by charge noise induced by nearby surfaces. The current state of the art for indistinguishability are parametric down conversion single-photon sources, but they intrinsically generate multiphoton events and hence must be operated at very low brightness to maintain high single photon purity. To date, no technology has proven to be capable of providing a source that simultaneously generates near-unity indistinguishability and pure single photons with high brightness. Here, we report on such devices made of quantum dots in electrically controlled cavity structures. We demonstrate on-demand, bright and ultra-pure single photon generation. Application of an electrical bias on deterministically fabricated devices is shown to fully cancel charge noise effects. Under resonant excitation, an indistinguishability of {\$}0.9956\backslashpm0.0045{\$} is evidenced with a {\$}g{\^{}}{\{}2{\}}(0)=0.0028\backslashpm0.0012{\$}. The photon extraction of {\$}65{\%}{\$} and measured brightness of {\$}0.154\backslashpm0.015{\$} make this source {\$}20{\$} times brighter than any source of equal quality. This new generation of sources open the way to a new level of complexity and scalability in optical quantum manipulation.},
author = {Somaschi, N. and Giesz, V. and {De Santis}, L. and Loredo, J. C. and Almeida, M. P. and Hornecker, G. and Portalupi, S. L. and Grange, T. and Ant{\'{o}}n, C. and Demory, J. and G{\'{o}}mez, C. and Sagnes, I. and Lanzillotti-Kimura, N. D. and Lema{\'{i}}tre, A. and Auffeves, A. and White, A. G. and Lanco, L. and Senellart, P.},
doi = {10.1038/nphoton.2016.23},
file = {:C$\backslash$:/Users/1991l/Dropbox/2018 dissertation/reference papers/others/single photon generation/out{\_}somaschi2016{\_}insolidstate.pdf:pdf},
isbn = {1749-4885},
issn = {17494893},
journal = {Nature Photonics},
number = {5},
pages = {340--345},
title = {{Near-optimal single-photon sources in the solid state}},
volume = {10},
year = {2016}
}
@article{Eisenberg2005,
abstract = {Multiphoton path entanglement is created without applying postselection, by manipulating the state of stimulated parametric down-conversion. A specific measurement on one of the two output spatial modes leads to the nonlocal bunching of the photons of the other mode, forming the desired multiphoton path entangled state. We present experimental results for the case of a heralded two-photon path entangled state and show how to extend this scheme to higher photon numbers.},
author = {Eisenberg, H. S. and Hodelin, J. F. and Khoury, G. and Bouwmeester, D.},
doi = {10.1103/PhysRevLett.94.090502},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Eisenberg et al. - 2005 - Multiphoton path entanglement by nonlocal bunching(2).pdf:pdf},
isbn = {0031-9007},
issn = {00319007},
journal = {Physical Review Letters},
number = {9},
pages = {090502},
pmid = {15783951},
title = {{Multiphoton path entanglement by nonlocal bunching}},
volume = {94},
year = {2005}
}
@article{Nasr2009,
abstract = {Quantum optical coherence tomography (QOCT) makes use of an entangled-photon light source to carry out dispersion-immune axial optical sectioning. We present the first experimental QOCT images of a biological sample: an onion-skin tissue coated with gold nanoparticles. 3D images are presented in the form of 2D sections of different orientations. In the context of quantum information, this represents the first experiment in which a quantum-entangled entity interacts with a biological specimen, generating a collection of quantum interferograms, from which an image is constructed. {\textcopyright} 2008 Elsevier B.V. All rights reserved.},
author = {Nasr, Magued B. and Goode, Darryl P. and Nguyen, Nam and Rong, Guoxin and Yang, Linglu and Reinhard, Bj{\"{o}}rn M. and Saleh, Bahaa E.A. and Teich, Malvin C.},
doi = {10.1016/j.optcom.2008.11.061},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Nasr et al. - 2009 - Quantum optical coherence tomography of a biological sample(2).pdf:pdf},
isbn = {0030-4018},
issn = {00304018},
journal = {Optics Communications},
number = {6},
pages = {1154--1159},
title = {{Quantum optical coherence tomography of a biological sample}},
volume = {282},
year = {2009}
}
@article{Hofheinz2008,
abstract = {We demonstrate the controlled generation of Fock states with up to 15 photonsin a microwave coplanar waveguide resonator coupled to a superconducting phasequbit. The subsequent decay of the Fock states, due to dissipation, is thenmonitored by varying the time delay between preparing the state and performinga number-state analysis. We find that the decay dynamics can be described by amaster equation where the lifetime of the n-photon Fock state scales as 1/n, inagreement with theory. We have also generated a coherent state in the microwaveresonator, and monitored its decay process. We demonstrate that the coherentstate maintains a Poisson distribution as it decays, with an average photonnumber that decreases with the same characteristic decay time as the one-photonFock state.},
author = {Hofheinz, Max and Weig, E. M. and Ansmann, M. and Bialczak, Radoslaw C. and Lucero, Erik and Neeley, M. and O'Connell, A. D. and Wang, H. and Martinis, John M. and Cleland, A. N.},
doi = {10.1038/nature07136},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Hofheinz et al. - 2008 - Generation of Fock states in a superconducting quantum circuit.pdf:pdf},
isbn = {1476-4687 (Electronic)$\backslash$n0028-0836 (Linking)},
issn = {14764687},
journal = {Nature},
number = {07136},
pages = {310--314},
pmid = {19113602},
title = {{Generation of Fock states in a superconducting quantum circuit}},
volume = {454},
year = {2008}
}
@article{Dowling2008,
author = {Dowling, Jonathan P},
doi = {10.1080/00107510802091298},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Dowling - 2017 - Quantum optical metrology – the lowdown on high-NOON states.pdf:pdf},
journal = {Contemporary physics},
number = {2},
pages = {125--143},
title = {{Quantum optical metrology – the lowdown on high-NOON states}},
volume = {49},
year = {2008}
}
@article{Zou2002,
author = {Zou, Xu Bo and Pahlke, K and Mathis, W},
doi = {http://dx.doi.org/10.1016/S0375-9601(02)01535-9},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Zou, Pahlke, Mathis - 2002 - Generation of multi-photon entangled states by using linear optical elements and a projective measurement.pdf:pdf},
issn = {0375-9601},
journal = {Physics Review A},
number = {1},
pages = {014102},
title = {{Generation of multi-photon entangled states by using linear optical elements}},
volume = {306},
year = {2002}
}
@article{Joo2012,
abstract = {We investigate the phase enhancement of quantum states subject to non-linear phase shifts. The optimal phase estimation of even entangled coherent states (ECSs) is shown to be better than that of NOON states and of odd ECS states with the same average particle number {\textless}n{\textgreater} and non-linearity exponent k. We investigate the creation of approximate ECSs (AECSs) from a squeezed vacuum with current optical technology methods and find that a pure AECS is even slightly better than an even ECS for large {\textless}n{\textgreater}. We also examine simple but physically relevant cases of loss in the non-linear interferometer arm, for a fixed {\textless}n{\textgreater}.},
author = {Joo, Jaewoo and Park, Kimin and Jeong, Hyunseok and Munro, William J. and Nemoto, Kae and Spiller, Timothy P.},
doi = {10.1103/PhysRevA.86.043828},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Joo et al. - 2012 - Quantum metrology for nonlinear phase shifts with entangled coherent states.pdf:pdf},
issn = {10502947},
journal = {Physical Review A},
number = {4},
pages = {043828},
title = {{Quantum metrology for nonlinear phase shifts with entangled coherent states}},
volume = {86},
year = {2012}
}
@article{Krischek2011,
abstract = {We experimentally demonstrate a general criterion to identify entangled states useful for the estimation of an unknown phase shift with a sensitivity higher than the shot-noise limit.We show how to exploit this entanglement on the examples of a maximum likelihood as well as of a Bayesian phase estimation protocol. Using an entangled four-photon state we achieve a phase sensitivity clearly beyond the shot- noise limit. Our detailed comparison of methods and quantum states for entanglement enhanced metrology reveals the connection between multiparticle entanglement and sub-shot-noise uncertainty, both in a frequentist and in a Bayesian phase estimation setting.},
author = {Krischek, Roland and Schwemmer, Christian and Wieczorek, Witlef and Weinfurter, Harald and Hyllus, Philipp and Pezz{\'{e}}, Luca and Smerzi, Augusto},
doi = {10.1103/PhysRevLett.107.080504},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Krischek et al. - 2011 - Useful multiparticle entanglement and sub-shot-noise sensitivity in experimental phase estimation.pdf:pdf},
isbn = {0031-9007 1079-7114},
issn = {00319007},
journal = {Physical Review Letters},
number = {8},
pages = {080504},
title = {{Useful multiparticle entanglement and sub-shot-noise sensitivity in experimental phase estimation}},
volume = {107},
year = {2011}
}
@article{Cui2013,
author = {Cui, Jin Ming and Sun, Fang Wen and Chen, Xiang Dong and Gong, Zhao Jun and Cuo, Guang Can},
doi = {10.1103/PhysRevLett.110.153901},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Cui et al. - 2013 - Quantum statistical imaging of particles without restriction of the diffraction limit.pdf:pdf},
isbn = {0031-9007$\backslash$n1079-7114},
issn = {00319007},
journal = {Physical Review Lettersc},
number = {15},
pages = {153901},
title = {{Quantum statistical imaging of particles without restriction of the diffraction limit}},
volume = {110},
year = {2013}
}
@article{Knott2016a,
abstract = {Quantum metrology has the potential to revolutionise precision measurements by going beyond the bounds of classical physics. However, in the optical applications which require a large photon flux, such as gravitational wave detection, the fragility of quantum states reduces the precision gains to small constant-factor improvements. Here we instead focus on the low photon number regime, which is relevant to measurements of delicate systems, and show that in this regime significant improvements can be gained over classical measurements. In particular, the scheme we propose achieves a precision with a {\$}\backslashsqrt{\{}7{\}}{\$} factor improvement over the classical limit, and a {\$}\backslashsqrt{\{}3{\}}{\$} improvement when compared to the quantum states commonly considered for enhanced phase estimation. Crucially, the procedure we propose employs probe states that have already been produced in experiments, and is robust to moderate losses.},
author = {Knott, P. A. and Proctor, T. J. and Hayes, A. J. and Cooling, J. P. and Dunningham, J. A.},
doi = {10.1103/PhysRevA.93.033859},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Knott et al. - 2016 - Practical quantum metrology with large precision gains in the low-photon-number regime.pdf:pdf},
issn = {24699934},
journal = {Physical Review A},
number = {3},
pages = {033859},
title = {{Practical quantum metrology with large precision gains in the low-photon-number regime}},
volume = {93},
year = {2016}
}
@article{You2017,
author = {You, Chenglong and Adhikari, Sushovit and Chi, Yuxi and LaBorde, Margarite L. and Matyas, Corey T. and Zhang, Chenyu and Su, Zuen and Byrnes, Tim and Lu, Chaoyang and Dowling, Jonathan P. and Olson, Jonathan P.},
doi = {10.1088/2040-8986/aa9133},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/You et al. - 2017 - Multiparameter estimation with single photons - linearly-optically generated quantum entanglement beats the shotnois.pdf:pdf},
isbn = {9781557528209},
issn = {20408986},
journal = {Journal of Optics},
number = {12},
pages = {124002},
title = {{Multiparameter estimation with single photons - linearly-optically generated quantum entanglement beats the shotnoise limit}},
volume = {19},
year = {2017}
}
@article{Kapale2007,
abstract = {We propose a bootstrapping approach to the generation of maximally path-entangled states of photons, so-called “NOON states.” The strong atom-light interaction of cavity QED can be employed to generate NOON states with about 100 photons. These can then be used to boost the existing experimental Kerr nonlinearities based on quantum coherence effects, to facilitate NOON generation with an arbitrarily large number of photons. We also offer an alternative scheme that uses an atom-cavity dispersive interaction to obtain a sufficiently high Kerr nonlinearity necessary for arbitrary NOON generation.},
author = {Kapale, Kishore T. and Dowling, Jonathan P.},
doi = {10.1103/PhysRevLett.99.053602},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Kapale, Dowling - 2007 - Bootstrapping approach for generating maximally path-entangled photon states.pdf:pdf},
isbn = {1557528454},
issn = {00319007},
journal = {Physical Review Letters},
number = {5},
pages = {053602},
pmid = {17930751},
title = {{Bootstrapping approach for generating maximally path-entangled photon states}},
volume = {99},
year = {2007}
}
@article{Achilles2003,
author = {Achilles, Daryl and Silberhorn, Christine and Sliwa, Cezary and Banaszek, Konrad and Walmsley, Ian A.},
doi = {10.1364/OL.28.002387},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Achilles et al. - 2003 - Fiber-assisted detection with photon number resolution.pdf:pdf},
isbn = {1539-4794},
issn = {0146-9592},
journal = {Optics letters},
number = {23},
pages = {2387--2389},
pmid = {14680191},
title = {{Fiber-assisted detection with photon number resolution.}},
volume = {28},
year = {2003}
}
@article{Afek2010,
author = {Afek, Itai and Ambar, Oron and Silberberg, Yaron},
doi = {10.1126/science.1188172},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Afek, Ambar, Silberberg - 2010 - High-NOON States by Mixing Quantum and Classical Light.pdf:pdf},
isbn = {1095-9203 (Electronic) 0036-8075 (Linking)},
issn = {00368075},
journal = {Science},
number = {5980},
pages = {879--881},
pmid = {20466927},
title = {{High-NOON states by mixing quantum and classical light}},
volume = {328},
year = {2010}
}
@article{Lee2002a,
abstract = {Heisenberg-limited measurement protocols can be used to gain an increase in measurement precision over classical protocols. Such measurements can be implemented using, e.g., optical Mach-Zehnder interferometers and Ramsey spectroscopes. We address the formal equivalence between the Mach-Zehnder interferometer, the Ramsey spectroscope, and the discrete Fourier transform. Based on this equivalence we introduce the ``quantum Rosetta stone'', and we describe a projective-measurement scheme for generating the desired correlations between the interferometric input states in order to achieve Heisenberg-limited sensitivity. The Rosetta stone then tells us the same method should work in atom spectroscopy.},
author = {Lee, Hwang and Kok, Pieter and Dowling, Jonathan P.},
doi = {10.1080/0950034021000011536},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Lee, Kok, Dowling - 2002 - A quantum Rosetta stone for interferometry.pdf:pdf},
isbn = {0950034021000},
issn = {09500340},
journal = {Journal of Modern Optics},
number = {14/15},
pages = {2325--2338},
title = {{A quantum Rosetta stone for interferometry}},
volume = {49},
year = {2002}
}
@article{Lee2016,
abstract = {We address how a quantum phase estimation using a {\$}|\backslashphi 0\backslashrangle+|0\backslashphi\backslashrangle{\$}-type entangled state can be controllable by Mandel Q-factor of a single-mode state {\$}|\backslashphi\backslashrangle{\$}. From a simple form of the quantum Fisher information, we show that quantum Cram$\backslash$'er-Rao bound can be enhanced with super-Poissonianity of the single-mode component. For an optical phase estimation, these bounds can also be achieved in a certain range of unknown phases by performing a parity measurement at the output. On the other hand, over an entire range {\$}[0,2\backslashpi]{\$} of unknown phase shifts, we show that the phase-shift range for beating shot-noise limit can be enlarged with sub-Poissonianity of the single-mode component.},
author = {Lee, Su-yong and Lee, Chang-woo and Lee, Jaehak and Nha, Hyunchul},
doi = {10.1038/srep30306},
file = {:C$\backslash$:/Users/1991l/Dropbox/2018 dissertation/reference papers/others/srep30306{\_}lee2016.pdf:pdf},
issn = {2045-2322},
journal = {Scientiific Reports},
pages = {30306},
title = {{Quantum phase estimation using path-symmetric entangled states}},
volume = {6},
year = {2016}
}
@article{Wu1986,
abstract = {Squeezed states of the electromagnetic field are generated by degenerate parametric down conversion in an optical cavity. Noise reductions greater than 50{\%} relative to the vacuum noise level are observed in a balanced homodyne detector. A quantitative comparison with theory suggests that the observed squeezing results from a field that in the absence of linear attenuation would be squeezed by greater then tenfold.},
author = {Wu, Ling An and Kimble, H. J. and Hall, J. L. and Wu, Huifa},
doi = {10.1103/PhysRevLett.57.2520},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Wu et al. - 1986 - Generation of squeezed states by parametric down conversion.pdf:pdf},
isbn = {1079-7114 (Electronic)$\backslash$r0031-9007 (Linking)},
issn = {00319007},
journal = {Physical Review Letters},
number = {20},
pages = {2520},
pmid = {10033788},
title = {{Generation of squeezed states by parametric down conversion}},
volume = {57},
year = {1986}
}
@book{Helstrom1976,
address = {New York},
author = {Helstrom, Carl W.},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Helstrom - 1976 - Quantum Detection and Estimation Theory.pdf:pdf},
publisher = {Academic},
title = {{Quantum detection and estimation theory}},
year = {1976}
}
@article{Israel2014,
abstract = {A quantum polarized light microscope using entangled NOON states with N ¼ 2 and N ¼ 3 is shown to provide phase supersensitivity beyond the standard quantum limit. We constructed such a microscope and imaged birefringent objects at a very low light level of 50 photons per pixel, where shot noise seriously hampers classical imaging. The NOON light source is formed by combining a coherent state with parametric down-converted light. We were able to show improved phase images with sensitivity close to the Heisenberg limit.},
author = {Israel, Yonatan and Rosen, Shamir and Silberberg, Yaron},
doi = {10.1103/PhysRevLett.112.103604},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Israel, Rosen, Silberberg - 2014 - Supersensitive polarization microscopy using noon states of light.pdf:pdf},
isbn = {0031-9007 1079-7114},
issn = {10797114},
journal = {Physical Review Letters},
number = {10},
pages = {103604},
title = {{Supersensitive polarization microscopy using NOON states of light}},
volume = {112},
year = {2014}
}
@article{Lee2015,
abstract = {It was recently shown that an entangled coherent state, which is a superposition of two different coherent states, can surpass the performance of N00N state in estimating an unknown phase-shift. This may hint at further enhancement in phase estimation by incorporating more component states in the superposition of resource state. We here study a four-headed cat state (4HCS), a superposition of four different coherent states, and propose its application to quantum phase estimation. We first investigate how the 4HCS is more nonclassical than a 2HCS in view of some nonclassical measures including sub-Poissonian statistics, negativity of Wigner distribution, and entanglement potential. We then demonstrate the enhanced performance in phase estimation by employing an entangled state via the 4HCS, which can surpass that of the 2HCS particularly in the regime of small average photon number. Moreover, we show that an entangled state modified from the 4HCS can further enhance the phase estimation even in the regime of large average photon number under a photon-loss channel. Our investigation further extends to incorporate an increasingly large number of component states in the resource superposition state and clearly show its merit in phase estimation.},
author = {Lee, Su-Yong and Lee, Chang-woo and Nha, Hyunchul and Kaszlikowski, Dagomir},
doi = {10.1364/JOSAB.32.001186},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Lee et al. - 2015 - Quantum phase estimation using a multi-headed cat state(2).pdf:pdf},
issn = {0740-3224},
journal = {Journal of the Optical Society of America B},
number = {6},
pages = {1186--1192},
title = {{Quantum phase estimation using a multi-headed cat state}},
volume = {32},
year = {2015}
}
@article{Shafiei2004,
abstract = {Three-photon entangled states such as a Greenberger-Horne-Zeilinger state can be produced by mixing a weak coherent state with parametric down-conversion. Quantum interference between the two states is responsible for the cancellation of unwanted photon states. Two schemes of interference are considered and both are shown to produce the entangled state.},
author = {Shafiei, F. and Srinivasan, P. and Ou, Z. Y.},
doi = {10.1103/PhysRevA.70.043803},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Shafiei, Srinivasan, Ou - 2004 - Generation of three-photon entangled state by quantum interference between a coherent state and para(2).pdf:pdf},
issn = {1050-2947},
journal = {Physical Review A},
number = {4},
pages = {043803},
title = {{Generation of three-photon entangled state by quantum interference between a coherent state and parametric down-conversion}},
volume = {70},
year = {2004}
}
@article{Birrittella2012,
abstract = {We study multiphoton quantum-interference effects at a beam splitter and its connection to the prospect of attaining interferometric phase-shift measurements with noise levels below the standard quantum limit. Specifically,we consider themixing of the most classical states of light coherent states with the most nonclassical states of light number states at a 50 : 50 beam splitter. Multiphoton quantum-interference effects from mixing photon-number states of small photon numbers with coherent states of arbitrary amplitudes are dramatic even at the level of a single photon. For input vacuum and coherent states, the joint photon-number distribution after the beam splitter is unimodal, a product of Poisson distributions for each of the output modes but with the input of a single photon, the original distribution is symmetrically bifurcated into a bimodal distribution. With a two-photon-number state mixed with a coherent state, a trimodal distribution is obtained, etc. The obtained distributions are shown to be structured so as to be conducive for approaching Heisenberg-limited sensitivities in photon-number parity-based interferometry.We show that mixing a coherent state with even a single photon results in a significant reduction in noise over that of the shot-noise limit. Finally, based on the results of mixing coherent light with single photons, we consider the mixing coherent light with the squeezed vacuum and the squeezed one-photon states and find the latter yields higher sensitivity in phase-shift measurements for the same squeeze parameter owing to the absence of the vacuum state.},
author = {Birrittella, Richard and Mimih, Jihane and Gerry, Christopher C.},
doi = {10.1103/PhysRevA.86.063828},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Birrittella, Mimih, Gerry - 2012 - Multiphoton quantum interference at a beam splitter and the approach to Heisenberg-limited interferom.pdf:pdf},
issn = {10502947},
journal = {Physical Review A},
number = {6},
pages = {063828},
title = {{Multiphoton quantum interference at a beam splitter and the approach to Heisenberg-limited interferometry}},
volume = {86},
year = {2012}
}
@article{Bollinger1996,
abstract = {We show how maximally correlated states of N two-level particles can be used in spectroscopy to yield a frequency uncertainty equal to (NT)-1, where T is the time of a single measurement. From the time-energy uncertainty relation we show that this is the best precision possible. We rephrase these results in the language of particle interferometry and obtain a state and detection operator which can be used to achieve a phase uncertainty exactly equal to the 1/N Heisenberg limit, where N is the number of particles used in the measurement.},
author = {Bollinger, J. J. and Itano, Wayne M. and Wineland, D. J. and Heinzen, D. J.},
doi = {10.1103/PhysRevA.54.R4649},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Bollinger et al. - 1996 - Optimal frequency measurements with maximally correlated states.pdf:pdf},
issn = {10941622},
journal = {Physical Review A},
number = {6},
pages = {R4649--R4652},
pmid = {9914139},
title = {{Optimal frequency measurements with maximally correlated states}},
volume = {54},
year = {1996}
}
@article{Okamoto2008,
abstract = {Quantum metrology promises greater sensitivity for optical phase measurements than could ever be achieved classically. Here we present a theory of the phase sensitivity for the general case where the detection probability is given by an {\$}N{\$} photon interference fringe. We find that the phase sensitivity has a complex dependence on both the intrinsic efficiency of detection {\$}\backslasheta{\$} and the interference fringe visibility {\$}V{\$}. Most importantly, the phase that gives maximum phase sensitivity is in general not the same as the phase at which the slope of the interference fringe is a maximum, as has previously been assumed. We determine the parameter range where quantum enhanced sensitivity can be achieved. In order to illustrate these theoretical results, we perform a four photon experiment with {\$}\backslasheta=3/4{\$} and {\$}V=82\backslashpm6{\$}{\%} (an extension of our previous work [Science $\backslash$textbf{\{}316{\}}, 726 (2007)]) and find a phase sensitivity 1.3 times greater than the standard quantum limit at a phase different to that which gives maximum slope of the interference fringe.},
author = {Okamoto, Ryo and Hofmann, Holger F. and Nagata, Tomohisa and O'Brien, Jeremy L. and Sasaki, Keiji and Takeuchi, Shigeki},
doi = {10.1088/1367-2630/10/7/073033},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Okamoto et al. - 2008 - Beating the standard quantum limit Phase super-sensitivity of N-photon interferometers.pdf:pdf},
isbn = {1367-2630},
issn = {13672630},
journal = {New Journal of Physics},
number = {7},
pages = {073033},
title = {{Beating the standard quantum limit: phase super-sensitivity of N-photon interferometers}},
volume = {10},
year = {2008}
}
@article{Giovannetti2004,
abstract = {Quantum mechanics, through the Heisenberg uncertainty principle, imposes limits on the precision of measurement. Conventional measurement techniques typically fail to reach these limits. Conventional bounds to the precision of measurements such as the shot noise limit or the standard quantum limit are not as fundamental as the Heisenberg limits and can be beaten using quantum strategies that employ "quantum tricks" such as squeezing and entanglement.},
author = {Giovannetti, Vittorio and Lloyd, Seth and Maccone, Lorenzo},
doi = {10.1126/science.1104149},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Giovannetti, Lloyd, Maccone - 2004 - Quantum Enhanced Measurement Beating the Standard Quantum Limit.pdf:pdf},
isbn = {0036-8075},
issn = {0036-8075},
journal = {Science},
number = {5700},
pages = {1330--1336},
pmid = {15550661},
title = {{Quantum enhanced measurement: beating the standard quantum limit}},
volume = {306},
year = {2004}
}
@article{Horodecki2009,
abstract = {All our former experience with application of quantum theory seems to say that what is predicted by quantum formalism must occur in the laboratory. But the essence of quantum formalism—entanglement, recognized by Einstein, Podolsky, Rosen, and Schr{\"{o}}dinger—waited over 70years to enter laboratories as a new resource as real as energy. This holistic property of compound quantum systems, which involves nonclassical correlations between subsystems, has potential for many quantum processes, including canonical ones: quantum cryptography, quantum teleportation, and dense coding. However, it appears that this new resource is complex and difficult to detect. Although it is usually fragile to the environment, it is robust against conceptual and mathematical tools, the task of which is to decipher its rich structure. This article reviews basic aspects of entanglement including its characterization, detection, distillation, and quantification. In particular, various manifestations of entanglement via Bell inequalities, entropic inequalities, entanglement witnesses, and quantum cryptography are discussed, and some interrelations are pointed out. The basic role of entanglement in quantum communication within a distant laboratory paradigm is stressed, and some peculiarities such as the irreversibility of entanglement manipulations are also discussed including its extremal form—the bound entanglement phenomenon. The basic role of entanglement witnesses in detection of entanglement is emphasized.},
author = {Horodecki, Ryszard and Horodecki, Pawe{\l} and Horodecki, Micha{\l} and Horodecki, Karol},
doi = {10.1103/RevModPhys.81.865},
isbn = {0034-6861$\backslash$r1539-0756},
issn = {00346861},
journal = {Reviews of Modern Physics},
number = {2},
pages = {865--942},
title = {{Quantum entanglement}},
volume = {81},
year = {2009}
}
@article{Lee2002,
abstract = {We propose a method for preparing maximal path entanglement with a definite photon number N, larger than two, using projective measurements. In contrast with the previously known schemes, our method uses only linear optics. Specifically, we exhibit a way of generating four-photon, path-entangled states of the form |4,0{\textgreater} + |0,4{\textgreater}, using only four beam splitters and two detectors. These states are of major interest as a resource for quantum interferometric sensors as well as for optical quantum lithography and quantum holography.},
author = {Lee, Hwang and Kok, Pieter and Cerf, Nicolas J. and Dowling, Jonathan P.},
doi = {10.1103/PhysRevA.65.030101},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Lee et al. - 2002 - Linear optics and projective measurements alone suffice to create large-photon-number path entanglement.pdf:pdf},
isbn = {1050-2947$\backslash$n1094-1622},
issn = {10941622},
journal = {Physical Review A},
number = {3},
pages = {030101},
title = {{Linear optics and projective measurements alone suffice to create large-photon-number path entanglement}},
volume = {65},
year = {2002}
}
@article{Tsang2009,
abstract = {I propose a quantum imaging method that can beat the Rayleigh-Abbe diffraction limit and achieve de Broglie resolution without requiring a multiphoton absorber as the detector. Using the same non-classical states of light as those for quantum lithography, the proposed method requires only intensity measurements, followed by image post-processing, to produce the same complex image patterns as those in quantum lithography. The method is expected to be experimentally realizable using current technology.},
author = {Tsang, Mankei},
doi = {10.1103/PhysRevLett.102.253601},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Tsang - 2009 - Quantum imaging beyond the diffraction limit by optical centroid measurements.pdf:pdf},
issn = {00319007},
journal = {Physical Review Letters},
number = {25},
pages = {253601},
pmid = {19659073},
title = {{Quantum imaging beyond the diffraction limit by optical centroid measurements}},
volume = {102},
year = {2009}
}
@incollection{GHZ1989,
abstract = {Bell's Theorem proved that one cannot in general reproduce the results of quantum theory with a classical, deterministic local model. However, Einstein originally considered the case where one could define an 'element of reality', namely for the much simpler case where one could predict with certainty a definite outcome for an experiment. For this simple case, Bell's Theorem says nothing. But by using a slightly more complicated model than Bell, one can show that even in this simple case where one can make definite predictions, one still cannot generally introduce deterministic, local models to explain the results.},
address = {Dordrecht},
author = {Greenberger, Daniel M. and Horne, Michael A. and Zeilinger, Anton},
booktitle = {Bell's Theorem, Quantum Theory and Conceptions of the Universe},
doi = {10.1007/978-94-017-0849-4_10},
file = {:C$\backslash$:/Users/1991l/Dropbox/2018 dissertation/reference papers/others/0712.0921{\_}GHZ1989.pdf:pdf},
isbn = {978-90-481-4058-9},
pages = {69--72},
publisher = {Springer},
title = {{Going beyond Bell's theorem}},
year = {1989}
}
@book{Miller1973,
author = {Miller, Willard},
publisher = {Academic Press},
title = {{Symmetry groups and their applications}},
year = {1973}
}
@article{Vahlbruch2016,
abstract = {Squeezed states of light belong to the most prominent nonclassical resources. They have compelling applications in metrology, which has been demonstrated by their routine exploitation for improving the sensitivity of a gravitational-wave detector since 2010. Here, we report on the direct measurement of 15 dB squeezed vacuum states of light and their application to calibrate the quantum efficiency of photoelectric detection. The object of calibration is a customized InGaAs positive intrinsic negative (p-i-n) photodiode optimized for high external quantum efficiency. The calibration yields a value of 99.5{\%} with a 0.5{\%} (k ¼ 2) uncertainty for a photon flux of the order 10 17 s −1 at a wavelength of 1064 nm. The calibration neither requires any standard nor knowledge of the incident light power and thus represents a valuable application of squeezed states of light in quantum metrology.},
author = {Vahlbruch, Henning and Mehmet, Moritz and Danzmann, Karsten and Schnabel, Roman},
doi = {10.1103/PhysRevLett.117.110801},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Vahlbruch et al. - 2016 - Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectri.pdf:pdf},
issn = {10797114},
journal = {Physical Review Letters},
number = {11},
pages = {110801},
title = {{Detection of 15 dB squeezed states of light and their application for the absolute calibration of photoelectric quantum efficiency}},
volume = {117},
year = {2016}
}
@article{Truax1985,
abstract = {For squeeze operators, an alternative to the matrix derivations of Baker-Campbell-Hausdorff relations is presented for the groups SU(2) and SU(1,1). The technique involves the solution of a system of nonlinear, first-order differential equations. By this method, criteria for unitarity of the representations are established, and these apply to both infinite- and to finite-dimensional representations of these groups.},
author = {Truax, D. R.},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Truax - 1985 - Baker-Campbell-Hausdorff relations and unitarity of SU (2) and SU (1, 1) squeeze operators.pdf:pdf},
journal = {Physical Review D},
number = {8},
pages = {1988},
title = {{Baker-Campbell-Hausdorff relations and unitarity of SU (2) and SU (1, 1) squeeze operators}},
volume = {31},
year = {1985}
}
@article{Motes2015,
abstract = {Quantum number-path entanglement is a resource for super-sensitive quantum metrology and in particular provides for sub-shotnoise or even Heisenberg-limited sensitivity. However, such number-path entanglement has thought to have been resource intensive to create in the first place --- typically requiring either very strong nonlinearities, or nondeterministic preparation schemes with feed-forward, which are difficult to implement. Very recently, arising from the study of quantum random walks with multi-photon walkers, as well as the study of the computational complexity of passive linear optical interferometers fed with single-photon inputs, it has been shown that such passive linear optical devices generate a superexponentially large amount of number-path entanglement. A logical question to ask is whether this entanglement may be exploited for quantum metrology. We answer that question here in the affirmative by showing that a simple, passive, linear-optical interferometer --- fed with only uncorrelated, single-photon inputs, coupled with simple, single-mode, disjoint photodetection --- is capable of significantly beating the shotnoise limit. Our result implies a pathway forward to practical quantum metrology with readily available technology.},
author = {Motes, Keith R. and Olson, Jonathan P. and Rabeaux, Evan J. and Dowling, Jonathan P. and Olson, S. Jay and Rohde, Peter P.},
doi = {10.1103/PhysRevLett.114.170802},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Motes et al. - 2015 - Linear Optical Quantum Metrology with Single Photons Exploiting Spontaneously Generated Entanglement to Beat the S.pdf:pdf},
isbn = {0031-9007},
issn = {10797114},
journal = {Physical Review Letters},
number = {17},
pages = {170802},
pmid = {25978219},
title = {{Linear optical quantum metrology with single photons: exploiting spontaneously generated entanglement to beat the shot-noise limit}},
volume = {114},
year = {2015}
}
@article{Gagatsos2016,
abstract = {For a fixed average energy, the simultaneous estimation of multiple phases can provide a better total precision than estimating them individually. We show this for a multimode interferometer with a phase in each mode, using Gaussian inputs and passive elements, by calculating the covariance matrix. The quantum Cram$\backslash$'{\{}e{\}}r-Rao bound provides a lower bound to the covariance matrix via the quantum Fisher information matrix, whose elements we derive to be the covariances of the photon numbers across the modes. We find our simultaneous strategy to yield no more than a factor of two improvement in total precision. In spite of the Gaussian nature of the problem, these elements require the calculation of non-Gaussian integrals, which we accomplish analytically. We prove that this bound can be saturated. Our work shows that no modal entanglement is necessary for simultaneous quantum-enhanced estimation of multiple phases.},
author = {Gagatsos, Christos N. and Branford, Dominic and Datta, Animesh},
doi = {10.1103/PhysRevA.94.042342},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Gagatsos, Branford, Datta - 2016 - Gaussian systems for quantum-enhanced multiple phase estimation.pdf:pdf},
issn = {24699934},
journal = {Physical Review A},
number = {4},
pages = {042342},
title = {{Gaussian systems for quantum-enhanced multiple phase estimation}},
volume = {94},
year = {2016}
}
@book{Scully1997,
author = {Scully, Marlan O. and Zubairy, M. Suhail},
publisher = {Cambridge University Press},
title = {{Quantum optics}},
year = {1997}
}
@article{Michler2000,
abstract = {Quantum communication relies on the availability of light pulses with strong quantum correlations among photons. An example of such an optical source is a single-photon pulse with a vanishing probability for detecting two or more photons. Using pulsed laser excitation of a single quantum dot, a single-photon turnstile device that generates a train of single-photon pulses was demonstrated. For a spectrally isolated quantum dot, nearly 100{\%} of the excitation pulses lead to emission of a single photon, yielding an ideal single-photon source.},
author = {Michler, P and Kiraz, A and Becher, C and Schoenfeld, W V and Petroff, P M and Zhang, Lidong and Hu, E and Imamoglu, A},
doi = {10.1126/science.290.5500.2282},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Michler et al. - 2000 - A quantum dot single-photon turnstile device.pdf:pdf},
isbn = {4351250763},
issn = {0036-8075},
journal = {Science},
number = {5500},
pages = {2282--2285},
pmid = {11125136},
title = {{A quantum dot single-photon turnstile device}},
volume = {290},
year = {2000}
}
@article{Baumgratz2016,
author = {Baumgratz, Tillmann and Datta, Animesh},
doi = {10.1103/PhysRevLett.116.030801},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Baumgratz, Datta - 2016 - Quantum Enhanced Estimation of a Multidimensional Field.pdf:pdf},
issn = {10797114},
journal = {Physical Review Letters},
number = {3},
pages = {030801},
pmid = {26849579},
title = {{Quantum enhanced estimation of a multidimensional field}},
volume = {116},
year = {2016}
}
@article{Nielsen2007,
abstract = {We propose a measurement protocol to generate path-entangled NOON states conditionally from two pulsed type II optical parametric oscillators. We calculate the fidelity of the produced states and the success probability of the protocol. The trigger detectors are assumed to have finite dead time, and for short pulse trigger fields they are modeled as on/off detectors with finite efficiency. Continuous-wave operation of the parametric oscillators is also considered.},
author = {Nielsen, Anne E B and M{\o}lmer, Klaus},
doi = {10.1103/PhysRevA.75.063803},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Nielsen, M{\o}lmer - 2007 - Conditional generation of path-entangled optical N,0 0,Nstates.pdf:pdf},
issn = {10502947},
journal = {Physical Review A},
number = {6},
pages = {063803},
title = {{Conditional generation of path-entangled optical |N,0{\textgreater} + |0,N{\textgreater} states}},
volume = {75},
year = {2007}
}
@article{Xiang2013,
abstract = {Quantum entanglement can help to increase the precision of optical phase measurements beyond the shot noise limit (SNL) to the ultimate Heisenberg limit. However, the N-photon parity measurements required to achieve this optimal sensitivity are extremely difficult to realize with current photon detection technologies, requiring high-fidelity resolution of N + 1 different photon distributions between the output ports. Recent experimental demonstrations of precision beyond the SNL have therefore used only one or two photon-number detection patterns instead of parity measurements. Here we investigate the achievable phase sensitivity of the simple and efficient single interference fringe detection technique. We show that the maximally-entangled "NOON" state does not achieve optimal phase sensitivity when N {\textgreater} 4, rather, we show that the Holland-Burnett state is optimal. We experimentally demonstrate this enhanced sensitivity using a single photon-counted fringe of the six-photon Holland-Burnett state. Specifically, our single-fringe six-photon measurement achieves a phase variance three times below the SNL.},
author = {Xiang, G. Y. and Hofmann, H. F. and Pryde, G. J.},
doi = {10.1038/srep02684},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Xiang, Hofmann, Pryde - 2013 - Optimal multi-photon phase sensing with a single interference fringe.pdf:pdf},
isbn = {9781557529398},
issn = {20452322},
journal = {Scientific Reports},
pages = {2684},
pmid = {24067490},
title = {{Optimal multi-photon phase sensing with a single interference fringe}},
volume = {3},
year = {2013}
}
@book{Cramer2016,
author = {Cram{\'{e}}r, Harald},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Cram{\'{e}}r - 2016 - Mathematical methods of statistics (PMS-9).pdf:pdf},
publisher = {Princeton university press},
title = {{Mathematical methods of statistics (PMS-9)}},
year = {2016}
}
@article{Ono2008,
author = {Ono, Takafumi and Hofmann, Holger F.},
doi = {10.1088/0953-4075/41/9/095502},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Ono, Hofmann - 2008 - Quantum enhancement of N-photon phase sensitivity by interferometric addition of down-converted photon pairs to we.pdf:pdf},
issn = {09534075},
journal = {Journal of Physics B: Atomic, Molecular and Optical Physics},
number = {9},
pages = {095502},
title = {{Quantum enhancement of N-photon phase sensitivity by interferometric addition of down-converted photon pairs to weak coherent light}},
volume = {41},
year = {2008}
}
@article{Motes2016,
abstract = {Fock states are a fundamental resource for many quantum technologies such as quantum metrology. While much progress has been made in single-photon source technologies, preparing Fock states with large photon number remains challenging. We present and analyze a bootstrapped approach for non-deterministically preparing large photon-number Fock states by iteratively fusing smaller Fock states on a beamsplitter. We show that by employing state recycling we are able to exponentially improve the preparation rate over conventional schemes, allowing the efficient preparation of large Fock states. The scheme requires single-photon sources, beamsplitters, number-resolved photo-detectors, fast-feedforward, and an optical quantum memory.},
author = {Motes, Keith R. and Mann, Ryan L. and Olson, Jonathan P. and Studer, Nicholas M. and Bergeron, E. Annelise and Gilchrist, Alexei and Dowling, Jonathan P. and Berry, Dominic W. and Rohde, Peter P.},
doi = {10.1103/PhysRevA.94.012344},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Motes et al. - 2016 - Efficient recycling strategies for preparing large Fock states from single-photon sources Applications to quantum.pdf:pdf},
issn = {24699934},
journal = {Physical Review A},
number = {1},
pages = {012344},
title = {{Efficient recycling strategies for preparing large Fock states from single-photon sources: applications to quantum metrology}},
volume = {94},
year = {2016}
}
@article{Ono2013,
author = {Ono, Takafumi and Okamoto, Ryo and Takeuchi, Shigeki},
doi = {10.1038/ncomms3426},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Ono, Okamoto, Takeuchi - 2013 - An entanglement-enhanced microscope.pdf:pdf},
journal = {Nature Communications},
pages = {3426},
title = {{An entanglement-enhanced microscope}},
volume = {4},
year = {2013}
}
@article{Ono2010,
abstract = {Two path interferometry with coherent states and squeezed vacuum can achieve phase sensitivities close to the Heisenberg limit when the average photon number of the squeezed vacuum is close to the average photon number of the coherent light. Here, we investigate the phase sensitivity of such states in the presence of photon losses. It is shown that the Cramer-Rao bound of phase sensitivity can be achieved experimentally by using a weak local oscillator and photon counting in the output. The phase sensitivity is then given by the Fisher information F of the state. In the limit of high squeezing, the ratio (F-N)/N{\^{}}2 of Fisher information above shot noise to the square of the average photon number N depends only on the average number of photons lost, n{\_}loss, and the fraction of squeezed vacuum photons mu. For mu=1/2, the effect of losses is given by (F-N)/N{\^{}}2=1/(1+2 n{\_}loss). The possibility of increasing the robustness against losses by lowering the squeezing fraction mu is considered and an optimized result is derived. However, the improvements are rather small, with a maximal improvement by a factor of two at high losses.},
author = {Ono, Takafumi and Hofmann, Holger F.},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Ono, Hofmann - 2010 - Effects of photon losses on phase estimation near the Heisenberg limit using coherent light and squeezed vacuum.pdf:pdf},
journal = {Physical Review A},
number = {3},
pages = {033819},
title = {{Effects of photon losses on phase estimation near the Heisenberg limit using coherent light and squeezed vacuum}},
volume = {81},
year = {2010}
}
@article{Taylor2016,
abstract = {Quantum metrology provides a route to overcome practical limits in sensing devices. It holds particular relevance to biology, where sensitivity and resolution constraints restrict applications both in fundamental biophysics and in medicine. Here, we review quantum metrology from this biological context, focusing on optical techniques due to their particular relevance for biological imaging, sensing, and stimulation. Our understanding of quantum mechanics has already enabled important applications in biology, including positron emission tomography (PET) with entangled photons, magnetic resonance imaging (MRI) using nuclear magnetic resonance, and bio-magnetic imaging with superconducting quantum interference devices (SQUIDs). In quantum metrology an even greater range of applications arise from the ability to not just understand, but to engineer, coherence and correlations at the quantum level. In the past few years, quite dramatic progress has been seen in applying these ideas into biological systems. Capabilities that have been demonstrated include enhanced sensitivity and resolution, immunity to imaging artefacts and technical noise, and characterization of the biological response to light at the single-photon level. New quantum measurement techniques offer even greater promise, raising the prospect for improved multi-photon microscopy and magnetic imaging, among many other possible applications. Realization of this potential will require cross-disciplinary input from researchers in both biology and quantum physics. In this review we seek to communicate the developments of quantum metrology in a way that is accessible to biologists and biophysicists, while providing sufficient details to allow the interested reader to obtain a solid understanding of the field. We further seek to introduce quantum physicists to some of the central challenges of optical measurements in biological science. We hope that this will aid in bridging the communication gap that exists between the fields, and thereby guide the future development of this multidisciplinary research area.},
author = {Taylor, Michael A. and Bowen, Warwick P.},
doi = {10.1016/j.physrep.2015.12.002},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Taylor, Bowen - 2016 - Quantum metrology and its application in biology.pdf:pdf},
issn = {03701573},
journal = {Physics Reports},
keywords = {Biology,Cell,Coherence,NOON state,Quantum Fisher information,Quantum correlations,Quantum metrology,Shot noise,Squeezed state},
pages = {1--59},
publisher = {Elsevier B.V.},
title = {{Quantum metrology and its application in biology}},
volume = {615},
year = {2016}
}
@article{Jarzyna2012,
abstract = {We discuss the role of an external phase reference in quantum interferometry. We point out inconsistencies in the literature with regard to the use of the quantum Fisher information (QFI) in phase estimation interferometric schemes. We discuss the interferometric schemes with and without an external phase reference and show a proper way to use QFI in both situations.},
author = {Jarzyna, Marcin and Demkowicz-Dobrza{\'{n}}ski, Rafa{\l}},
doi = {10.1103/PhysRevA.85.011801},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Jarzyna, Demkowicz-Dobrza{\'{n}}ski - 2012 - Quantum interferometry with and without an external phase reference.pdf:pdf},
issn = {10502947},
journal = {Physical Review A},
number = {1},
pages = {011801},
title = {{Quantum interferometry with and without an external phase reference}},
volume = {85},
year = {2012}
}
@article{Zhang2016,
abstract = {A universal and optimal method for the polarimetry of light with arbitrary photon statistics is presented. The method is based on the continuous maximum-likelihood positive operator-valued measure (ML-POVM) for pure polarization states over the surface of the Bloch sphere. The success probability and the mean fidelity are used as the figures of merit to show its performance. The POVM is found to attain the collective bound of polarization estimation with respect to the mean fidelity. As demonstrations, explicit results for the N photon Fock state, the phase-randomized coherent state (Poisson distribution), and the thermal light are obtained. It is found that the estimation performances for the Fock state and the Poisson distribution are almost identical, while that for the thermal light is much worse. This suggests that thermal light leaks less information to an eavesdropper and hence could potentially provide more security in polarization-encoded quantum communication protocols than a single-mode laser beam as customarily considered. Finally, comparisons against an optimal adaptive measurement with classical communications are made to show the better and more stable performance of the continuous ML-POVM.},
author = {Zhang, Lu and Chan, Kam Wai Clifford and Verma, Pramode K.},
doi = {10.1103/PhysRevA.93.032137},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Zhang, Chan, Verma - 2016 - Universal optimal estimation of the polarization of light with arbitrary photon statistics.pdf:pdf},
issn = {24699934},
journal = {Physical Review A},
number = {3},
pages = {032137},
title = {{Universal optimal estimation of the polarization of light with arbitrary photon statistics}},
volume = {93},
year = {2016}
}
@article{Humphreys2013,
author = {Humphreys, Peter C. and Barbieri, Marco and Datta, Animesh and Walmsley, Ian A.},
doi = {10.1103/PhysRevLett.111.070403},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Humphreys et al. - 2013 - Quantum Enhanced Multiple Phase Estimation.pdf:pdf},
journal = {Physical Review Letters},
number = {7},
pages = {070403},
title = {{Quantum enhanced multiple phase estimation}},
volume = {111},
year = {2013}
}
@article{Zhang2017a,
abstract = {Multi-mode NOON states have been attracting increasing attentions recently for their abilities of obtaining supersensitive and superresolved measurements for simultaneous multiple-phase estimation. In this paper, four different methods of generating multi-mode NOON states with high photon number are proposed. The first method is a linear optical approach that makes use of the Fock state filtration to reduce lower-order Fock state terms from the coherent state inputs, which are jointly combined to produce a multi-mode NOON state with the triggering of single-photon coincidence detections (SPCD) and appropriate postselection. The other three methods (two linear and one nonlinear) use N photon Fock states as the inputs and require SPCD triggering only. All of the four methods can theoretically create a multi-mode NOON state with arbitrary photon number. Comparisons among these four methods were made with respect to the feasibility and efficiency. The first method is experi-mentally most feasible since it takes considerably fewer photonic operations and, more importantly, requires neither the use of high-N Fock states nor high-degree of nonlinearity.},
author = {Zhang, Lu and Chan, Kam Wai Clifford},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Zhang, Wai, Chan - 2017 - Scalable Generation of Multi-mode NOON States for Quantum Multiple-phase Estimation.pdf:pdf},
journal = {arXiv},
pages = {1712.00128},
title = {{Scalable generation of multi-mode NOON states for quantum multiple-phase estimation}},
year = {2017}
}
@book{Walls2007,
author = {Walls, Daniel F. and Milburn, Gerard J.},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Wall, Daniel F., Milburn - 2007 - Quantum Optics.pdf:pdf},
publisher = {Springer Science {\&} Business Media},
title = {{Quantum otics}},
year = {2007}
}
@article{Braunstein1994,
abstract = {By finding measurements that optimally resolve neighboring quantum states, we use statistical distinguishability to define a natural Riemannian metric on the space of quantum-mechanical density operators and to formulate uncertainty principles that are more general and more stringent than standard uncertainty principles.},
author = {Braunstein, Samuel L. and Caves, Carlton M.},
doi = {10.1103/PhysRevLett.72.3439},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Braunstein, Caves - 1994 - Statistical distance and the geometry of quantum states.pdf:pdf},
isbn = {0031-9007},
issn = {00319007},
journal = {Physical Review Letters},
number = {22},
pages = {3439--3443},
pmid = {10056200},
title = {{Statistical distance and the geometry of quantum states}},
volume = {72},
year = {1994}
}
@article{Wang2017,
abstract = {Boson sampling is considered as a strong candidate to demonstrate 'quantum computational supremacy' over classical computers. However, previous proof-of-principle experiments suffered from small photon number and low sampling rates owing to the inefficiencies of the single-photon sources and multiport optical interferometers. Here, we develop two central components for high-performance boson sampling: robust multiphoton interferometers with 99{\%} transmission rate and actively demultiplexed single-photon sources based on a quantum dot–micropillar with simultaneously high efficiency, purity and indistinguishability. We implement and validate three-, four-and five-photon boson sampling, and achieve sampling rates of 4.96 kHz, 151 Hz and 4 Hz, respectively, which are over 24,000 times faster than previous experiments. Our architecture can be scaled up for a larger number of photons and with higher sampling rates to compete with classical computers, and might provide experimental evidence against the extended Church–Turing thesis. Q uantum computers 1 can, in principle, solve certain problems faster than classical computers. Despite substantial progress in the past two decades 2–4 , building quantum machines that can actually outperform classical computers for some specific tasks —an important milestone termed 'quantum supremacy'—remains challenging. In the quest of demonstrating quantum supremacy, boson sampling, an intermediate (that is, non-universal) quantum computer model proposed by Aaronson and Arkhipov 5 , has received considerable interest as it requires fewer physical resources than building universal optical quantum computers 6 . A quantum boson-sampling machine can be realized by sending n indistinguishable single photons through a passive m-mode (m {\textgreater} n) interferometer, and sampling from the probabilis-tic output distribution. Mathematically, the probability amplitude of each output outcome is proportional to the permanent of a corre-sponding n × n submatrix, which is strongly believed to be intract-able because calculating the permanent is a so-called {\#}P-complete problem. Note that, however, boson sampling is itself not a {\#}P-complete problem, that is, the matrix permanent cannot be efficiently calculated. For a specifically defined task of sampling over the entire distribution, it is expected that a sufficiently large quantum boson-sampling machine cannot be efficiently simulated by classical computers 5,7,8 . In principle, a large-scale boson-sampling machine would constitute an effective disproof against a foundational tenet in computer science: the extended Church–Turing thesis, which postulates that all realistic physical systems can be efficiently simulated with a (classical) probabilistic Turing machine. To this end, an experimental roadmap for demonstrating quantum supremacy is to construct multiphoton boson-sampling machines with increasing number of input photons and faster sampling rates to compete with classical computers. However, the overall performance of previous proof-of-principle boson-sampling experiments 9–17 was limited due to the lack of high-quality single-photon sources and low-loss multimode circuits. For example, the most commonly used pseudo-single photons created using spontaneous parametric down-conversion 18 (SPDC) were intrinsi-cally probabilistic and mixed with multiphoton components. The SPDC probability was kept low (about a few per cent) to suppress the unwanted two-photon emission. The frequency correlation of the SPDC photon pairs and the inefficient collection into single-mode fibres further reduced the single-photon heralding efficiency to typically a low level of ∼1{\%} in previous work},
author = {Wang, Hui and He, Yu and Li, Yu Huai and Su, Zu En and Li, Bo and Huang, He Liang and Ding, Xing and Chen, Ming Cheng and Liu, Chang and Qin, Jian and Li, Jin Peng and He, Yu Ming and Schneider, Christian and Kamp, Martin and Peng, Cheng Zhi and H{\"{o}}fling, Sven and Lu, Chao Yang and Pan, Jian Wei},
doi = {10.1038/nphoton.2017.63},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Wang et al. - 2017 - High-efficiency multiphoton boson sampling.pdf:pdf},
isbn = {1749-4885},
issn = {17494893},
journal = {Nature Photonics},
number = {6},
pages = {361--365},
title = {{High-efficiency multiphoton boson sampling}},
volume = {11},
year = {2017}
}
@book{Agarwal2013,
author = {Agarwal, Girish S.},
file = {:C$\backslash$:/Users/1991l/Dropbox/2018 dissertation/reference papers/others/9781107006409{\_}frontmatter{\_}Agarwal.pdf:pdf},
publisher = {Cambridge University Press},
title = {{Quantum Optics}},
year = {2013}
}
@article{Schwartz2013,
abstract = {The optical diffraction limit imposes a bound on imaging resolution in classical optics. Over the last twenty years, many theoretical schemes have been presented for overcoming the diffraction barrier in optical imaging using quantum properties of light. Here, we demonstrate a quantum superresolution imaging method taking advantage of nonclassical light naturally produced in fluorescence microscopy due to photon antibunching, a fundamentally quantum phenomenon inhibiting simultaneous emission of multiple photons. Using a photon counting digital camera, we detect antibunching-induced second and third order intensity correlations and perform subdiffraction limited quantum imaging in a standard wide-field fluorescence microscope.},
author = {Schwartz, Osip and Levitt, Jonathan M. and Tenne, Ron and Itzhakov, Stella and Deutsch, Zvicka and Oron, Dan},
doi = {10.1021/nl402552m},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Schwartz et al. - 2013 - Superresolution microscopy with quantum emitters.pdf:pdf},
issn = {15306984},
journal = {Nano Letters},
keywords = {Superresolution,optical microscopy,photon antibunching,quantum dots,quantum imaging},
number = {12},
pages = {5832--5836},
pmid = {24195698},
title = {{Superresolution microscopy with quantum emitters}},
volume = {13},
year = {2013}
}
@article{Liu2015,
abstract = {Quantum Fisher information is a central quantity in quantum metrology. We discuss an alternative representation of quantum Fisher information for unitary parametrization processes. The highlight of this representation is that all information of parametrization transformation, i.e., the entire dynamical information, is totally involved in a Hermitian operator H. Utilizing this representation, quantum Fisher information is only determined by H and the initial state. We apply this representation in a collective spin system and show the specific expression of H. For a simple case, a spin-half system, the quantum Fisher information is given and the optimal states to access maximum quantum Fisher information are found. Furthermore, for an exponential form initial state, an analytical expression of quantum Fisher information by H operator is provided. The multiparameter quantum metrology is also considered and discussed utilizing this representation in the last.},
author = {Liu, Jing and Jing, Xiao Xing and Wang, Xiaoguang},
doi = {10.1038/srep08565},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Liu, Jing, Wang - 2015 - Quantum metrology with unitary parametrization processes.pdf:pdf},
issn = {20452322},
journal = {Scientific Reports},
pages = {8565},
pmid = {25708678},
title = {{Quantum metrology with unitary parametrization processes}},
volume = {5},
year = {2015}
}
@article{Matsumoto2002,
author = {Matsumoto, K.},
file = {:C$\backslash$:/Users/1991l/Dropbox/2018 dissertation/reference papers/others/K{\_}Matsumoto2002{\_}J.{\_}Phys.{\_}A{\%}3A{\_}Math.{\_}Gen.{\_}35{\_}307.pdf:pdf},
journal = {Journal of Physics A: Mathematical and Theoretical},
number = {13},
pages = {3111},
title = {{A new approach to the Cram{\'{e}}r–Rao-type bound of the pure-state model}},
volume = {35},
year = {2002}
}
@article{Heisenberg1927,
author = {Heisenberg, W.},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Heisenberg - 1927 - The actual content of quantum theoretical kinematics and mechanics.pdf:pdf},
title = {{The actual content of quantum theoretical kinematics and mechanics}},
year = {1927}
}
@article{Birrittella2014,
author = {Birrittella, Richard and Gerry, Christopher C.},
doi = {10.1364/JOSAB.31.000586},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Birrittella, Gerry - 2014 - Quantum optical interferometry via the mixing of coherent and photon-subtracted squeezed vacuum states of li.pdf:pdf},
issn = {0740-3224},
journal = {Journal of the Optical Society of America B},
number = {3},
pages = {586--593},
title = {{Quantum optical interferometry via the mixing of coherent and photon-subtracted squeezed vacuum states of light}},
volume = {31},
year = {2014}
}
@article{Sun2006,
author = {Sun, F. W. and Ou, Z. Y. and Guo, G. C.},
doi = {10.1103/PhysRevA.73.023808},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Sun, Ou, Guo - 2006 - Projection measurement of the maximally entangled N -photon state for a demonstration of the N -photon de Brogl(2).pdf:pdf},
issn = {10941622},
journal = {Physical Review A},
number = {2},
pages = {023808},
title = {{Projection measurement of the maximally entangled N -photon state for a demonstration of the N -photon de Broglie wavelength}},
volume = {73},
year = {2006}
}
@article{Ding2016,
abstract = {Scalable photonic quantum technologies require on-demand single-photon sources with simultaneously high levels of purity, indistinguishability, and efficiency. These key features, however, have only been demonstrated separately in previous experiments. Here, by s-shell pulsed resonant excitation of a Purcell-enhanced quantum dot-micropillar system, we deterministically generate resonance fluorescence single photons which, at pi pulse excitation, have an extraction efficiency of 66{\%}, single-photon purity of 99.1{\%}, and photon indistinguishability of 98.5{\%}. Such a single-photon source for the first time combines the features of high efficiency and near-perfect levels of purity and indistinguishabilty, and thus open the way to multi-photon experiments with semiconductor quantum dots.},
author = {Ding, Xing and He, Yu and Duan, Z. C. and Gregersen, Niels and Chen, M. C. and Unsleber, S. and Maier, S. and Schneider, Christian and Kamp, Martin and H{\"{o}}fling, Sven and Lu, Chao Yang and Pan, Jian Wei},
doi = {10.1103/PhysRevLett.116.020401},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Ding et al. - 2016 - On-Demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driv.pdf:pdf},
isbn = {0031-9007},
issn = {10797114},
journal = {Physical Review Letters},
number = {2},
pages = {020401},
pmid = {26824530},
title = {{On-Demand single photons with high extraction efficiency and near-unity indistinguishability from a resonantly driven quantum dot in a micropillar}},
volume = {116},
year = {2016}
}
@article{Holland1993,
author = {Holland, M. J. and Burnett, K.},
doi = {10.1103/PhysRevLett.70.694},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Holland, Burnett - 1993 - Interferometric detection of optical phase shifts at the Heisenberg limit.pdf:pdf},
isbn = {0031-9007$\backslash$n1079-7114},
issn = {0031-9007},
journal = {Physical Review Letters},
number = {9},
pages = {1355--1358},
pmid = {10054179},
title = {{Interferometric detection of optical phase shifts at the Heisenberg limit}},
volume = {71},
year = {1993}
}
@article{Kuhlmann2015,
abstract = {Developing a quantum photonics network requires a source of very-high-fidelity single photons. An outstanding challenge is to produce a transform-limited single-photon emitter to guarantee that single photons emitted far apart in the time domain are truly indistinguishable. This is particularly difficult in the solid-state as the complex environment is the source of noise over a wide bandwidth. A quantum dot is a robust, fast, bright and narrow-linewidth emitter of single photons; layer-by-layer growth and subsequent nano-fabrication allow the electronic and photonic states to be engineered. This represents a set of features not shared by any other emitter but transform-limited linewidths have been elusive. Here, we report transform-limited linewidths measured on second timescales, primarily on the neutral exciton but also on the charged exciton close to saturation. The key feature is control of the nuclear spins, which dominate the exciton dephasing via the Overhauser field.},
author = {Kuhlmann, Andreas V. and Prechtel, Jonathan H. and Houel, Julien and Ludwig, Arne and Reuter, Dirk and Wieck, Andreas D. and Warburton, Richard J.},
doi = {10.1038/ncomms9204},
file = {:C$\backslash$:/Users/1991l/Dropbox/2018 dissertation/reference papers/others/single photon generation/ncomms9204{\_}Kuhlmann2015{\_}quantumdot.pdf:pdf},
issn = {20411723},
journal = {Nature Communications},
pages = {8204},
pmid = {26348157},
publisher = {Nature Publishing Group},
title = {{Transform-limited single photons from a single quantum dot}},
volume = {6},
year = {2015}
}
@article{Hong1987,
author = {Hong, C. K. and Ou, Z. Y. and Mandel, L.},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Hong, Ou, Mandel - 1987 - Measurement of subpicosecond time intervals between two ohotons by interference.pdf:pdf},
journal = {Physical Review Letters},
number = {18},
pages = {2044},
title = {{Measurement of subpicosecond time intervals between two ohotons by interference}},
volume = {59},
year = {1987}
}
@article{Braunstein1996,
abstract = {The quantum-mechanical framework in which observables are associated with Hermitian operators is too narrow to discuss measurements of such important physical quantities as elapsed time or harmonic-oscillator phase. We introduce a broader framework that allows us to derive quantum-mechanical limits on the precision to which a parameter---e.g., elapsed time---may be determined via arbitrary data analysis of arbitrary measurements on {\$}N{\$} identically prepared quantum systems. The limits are expressed as generalized Mandelstam-Tamm uncertainty relations, which involve the operator that generates displacements of the parameter---e.g., the Hamiltonian operator in the case of elapsed time. This approach avoids entirely the problem of associating a Hermitian operator with the parameter. We illustrate the general formalism, first, with nonrelativistic uncertainty relations for spatial displacement and momentum, harmonic-oscillator phase and number of quanta, and time and energy and, second, with Lorentz-invariant uncertainty relations involving the displacement and Lorentz-rotation parameters of the Poincar$\backslash$'e group.},
author = {Braunstein, Samuel L. and Caves, Carlton M. and Milburn, Gerard J.},
doi = {10.1006/aphy.1996.0040},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Braunstein, Caves, Milburn - 1995 - Generalized uncertainty relations Theory, examples, and Lorentz invariance.pdf:pdf},
issn = {00034916},
journal = {Annals of Physics},
keywords = {135 173,1996,als of physics 247},
number = {0040},
pages = {135--173},
title = {{Generalized uncertainty relations: Theory, examples, and Lorentz invariance}},
volume = {247},
year = {1995}
}
@article{Karimi2015,
author = {Karimi, Ebrahim and Boyd, Robert W},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Karimi, Boyd - 2015 - Classical entanglement.pdf:pdf},
journal = {Science},
number = {6265},
pages = {1172--1174},
title = {{Classical entanglement?}},
volume = {350},
year = {2015}
}
@article{Joo2011,
abstract = {We present an improved phase estimation scheme employing entangled coherent states and demon- strate that the states give the smallest variance in the phase parameter in comparison to NOON, BAT and "optimal" states under perfect and lossy conditions. As these advantages emerge for very modest particle numbers, the optical version of entangled coherent state metrology is achievable with current technology.},
author = {Joo, Jaewoo and Munro, William J. and Spiller, Timothy P.},
doi = {10.1103/PhysRevLett.107.083601},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Joo, Munro, Spiller - 2011 - Quantum metrology with entangled coherent states(2).pdf:pdf},
isbn = {0031-9007},
issn = {00319007},
journal = {Physical Review Letters},
number = {8},
pages = {083601},
pmid = {21929166},
title = {{Quantum metrology with entangled coherent states}},
volume = {107},
year = {2011}
}
@article{Wei2014,
abstract = {Single photons are attractive candidates of quantum bits (qubits) for quantum computation and are the best messengers in quantum networks. Future scalable, fault-tolerant photonic quantum technologies demand both stringently high levels of photon indistinguishability and generation efficiency. Here, we demonstrate deterministic and robust generation of pulsed resonance fluorescence single photons from a single semiconductor quantum dot using adiabatic rapid passage, a method robust against fluctuation of driving pulse area and dipole moments of solid-state emitters. The emitted photons are background-free, have a vanishing two-photon emission probability of 0.3{\%} and a raw (corrected) two-photon Hong?Ou?Mandel interference visibility of 97.9{\%} (99.5{\%}), reaching a precision that places single photons at the threshold for fault-tolerant surface-code quantum computing. This single-photon source can be readily scaled up to multiphoton entanglement and used for quantum metrology, boson sampling, and linear optical quantum computing.},
author = {Wei, Yu Jia and He, Yu Ming and Chen, Ming Cheng and Hu, Yi Nan and He, Y. and Wu, Dian and Schneider, Christian and Kamp, Martin and H{\"{o}}fling, Sven and Lu, Chao Yang and Pan, Jian Wei},
doi = {10.1021/nl503081n},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Wei et al. - 2014 - Deterministic and robust generation of single photons from a single quantum dot with 99.5{\%} indistinguishability usin.pdf:pdf},
isbn = {1530-6984},
issn = {15306992},
journal = {Nano Letters},
keywords = {adiabatic rapid passage,quantum computation,quantum dots,resonance fluorescence,single photons,two-photon interference},
number = {11},
pages = {6515--6519},
pmid = {25357153},
title = {{Deterministic and robust generation of single photons from a single quantum dot with 99.5{\%} indistinguishability using adiabatic rapid passage}},
volume = {14},
year = {2014}
}
@article{Shin2011,
abstract = {We demonstrate experimentally a new procedure for obtaining spatial super-resolution in quantum imaging by measuring optical centroid. Our results show spatial resolution enhancement identical to that of quantum lithography but with higher detection efficiency.},
author = {Shin, Heedeuk and Chan, Kam Wai Clifford and Chang, Hye Jeong and Boyd, Robert W.},
doi = {10.1103/PhysRevLett.107.083603},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Shin et al. - 2011 - Quantum spatial superresolution by optical centroid measurements.pdf:pdf},
isbn = {978-1-55752-910-7},
issn = {00319007},
journal = {Physical Review Letters},
number = {8},
pages = {083603},
pmid = {21929168},
title = {{Quantum spatial superresolution by optical centroid measurements}},
volume = {107},
year = {2011}
}
@book{Born2013,
author = {Born, Max and Wolf, Emil},
doi = {10.1002/9780470060193.ch2},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Born - Unknown - Principles of Optics.pdf:pdf},
isbn = {9780080264820},
issn = {00303992},
pmid = {25246403},
publisher = {Elsevier},
title = {{Principles of optics: electromagnetic theory of propagation, interference and diffraction of light}},
year = {2013}
}
@article{Zhang2017,
abstract = {The simultaneous multi-parameter estimation problem using a class of multi-mode entangled states is investigated in this paper. Specifically, the problem of optical phase imaging is considered and the quantum probe is taken to be a balanced coherent superposition of components with an arbitrary quantum state in one mode and vacuum states in all the other modes, which is a gener-alization of the multi-mode NOON state. The analytical form for the quantum Cram{\'{e}}r-Rao bound (QCRB) is presented, which shows the performance by providing a lower bound of the estimation uncertainty. It is shown that the NOON state has the worst performance among those in the class of the entangled states considered. We also analyze in detail four different scenarios, which are the NOON state, the entangled coherent state, the entangled squeezed coherent state, and the en-tangled squeezed vacuum state. From the comparison among these four states, we find that when the mean photon number is fixed, the squeezed vacuum state has the smallest QCRB, followed by the squeezed coherent state, entangled coherent state, and NOON state. We also illustrate that the balanced entangled state can perform better than a more generalized unbalanced form studied in previous works for certain scenarios. Finally, we give an experimental setup for producing a two-mode entangled state that can beat the NOON state in quantum metrology.},
author = {Zhang, Lu and Chan, Kam Wai Clifford},
doi = {10.1103/PhysRevA.95.032321},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Zhang, Chan - 2017 - Quantum multiparameter estimation with generalized balanced multimode NOON-like states.pdf:pdf},
issn = {24699934},
journal = {Physical Review A},
number = {3},
pages = {032321},
title = {{Quantum multiparameter estimation with generalized balanced multimode NOON-like states}},
volume = {95},
year = {2017}
}
@inproceedings{Zhang2018,
address = {in preparation},
author = {Zhang, Lu and Chan, Kam Wai Clifford},
title = {{Universal multi-mode NOON state generation using nondeterministic-photon-number inputs and post-selection}},
year = {2018}
}
@article{Dowling1998,
abstract = {I derive the quantum phase-noise limit to the sensitivity of a Mach-Zehnder interferometer in which the incident quantum particles enter via both input peas. I show that if the incident particles are entangled and correlated properly, then the phase sensitivity scales asymptotically like the Heisenberg-limited Delta phi = O(1/N), for large N, where N is the number of particles incident per unit time. (In a one-input-port device, the sensitivity can be at best Delta phi=1/root N.) My calculation applies to bosons or fermions of arbitrary integer or half-integer spin. Applications to optical, atom-beam, and atom-laser gyroscopes are discussed-in particular, an atom-laser can be used to obtain the required entanglements for achieving this Heisenberg-limited sensitivity with atomic matter waves.},
author = {Dowling, Jonathan P.},
doi = {10.1103/PhysRevA.57.4736},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Dowling - 1998 - Correlated input-port, matter-wave interferometer Quantum-noise limits to the atom-laser gyroscope.pdf:pdf},
issn = {10941622},
journal = {Physical Review A},
number = {6},
pages = {4736--4746},
pmid = {74160600083},
title = {{Correlated input-port, matter-wave interferometer: quantum-noise limits to the atom-laser gyroscope}},
volume = {57},
year = {1998}
}
@inproceedings{Zhang2018QCMC,
address = {Baton Rouge, LA},
author = {Zhang, Lu and Chan, Kam Wai Clifford},
booktitle = {Quantum Communication, Measurement and Computing (QCMC)},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Zhang, Chan - 2018 - Generation of multi-mode high-NOON states.pdf:pdf},
title = {{Generation of multi-mode high-NOON states}},
year = {2018}
}
@article{Kok2017,
author = {Kok, Pieter and Dunningham, Jacob and Ralph, Jason F.},
doi = {10.1103/PhysRevA.95.012326},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Kok, Dunningham, Ralph - 2017 - Role of entanglement in calibrating optical quantum gyroscopes.pdf:pdf},
issn = {24699934},
journal = {Physical Review A},
number = {1},
pages = {012326},
title = {{Role of entanglement in calibrating optical quantum gyroscopes}},
volume = {95},
year = {2017}
}
@article{Lita2008,
author = {Lita, Adriana E and Miller, Aaron J and Nam, Sae Woo},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Lita, Miller, Nam - 2008 - Counting near-infrared single-photons with 95{\%} efficiency.pdf:pdf},
journal = {Optics Express},
number = {5},
pages = {3032--3040},
title = {{Counting near-infrared single-photons with 95{\%} efficiency}},
volume = {16},
year = {2008}
}
@article{Kaneda2018,
abstract = {On-demand generation of indistinguishable single- and multi-photon states is a key technology for scaling up optical quantum information and communication applications. Nonlinear parametric photon-pair sources and heralded single-photon sources (HSPSs) had been the most standard resource of quantum information applications for decades. However, the intrinsic uncertainty of the produced number of photon pairs in such sources is a critical drawback that prevents on-demand photon-pair and heralded single-photon generation. Here we demonstrate large-scale time multiplexing of indistinguishable heralded single photons, employing a low-loss HSPS and adjustable delay line. We observed 66.7{\%} presence probability of single-photon states collected into a single-mode optical fiber by multiplexing 40 periodic time bins of heralded single photons. To our knowledge, this is the highest fiber-coupled single-photon probability achieved to date. A high indistinguishability ({\~{}}90{\%}) of our time-multiplexed photons has also been confirmed. We also experimentally investigate trade-off relations of single-photon probability and unwanted multi-photon contribution by using different pump powers for a HSPS. Our results demonstrate that low-loss, large-scale multiplexing can realize highly efficient single-photon generation as well as highly scalable multi-photon generation from inefficient HSPSs. We predict that our large-scale time multiplexing will pave the way toward generation of {\textgreater} 30 coincident photons with unprecedented efficiencies, enabling a new frontier in optical quantum information processing.},
author = {Kaneda, Fumihiro and Kwiat, Paul G.},
file = {:C$\backslash$:/Users/1991l/Dropbox/2018 dissertation/reference papers/others/single photon generation/1803.04803{\_}Kaneda2018{\_}timemultiplexing.pdf:pdf},
journal = {arXiv},
pages = {1803.04803},
title = {{High-efficiency single-photon generation via large-scale active time multiplexing}},
year = {2018}
}
@article{Giovannetti2009,
abstract = {No imaging apparatus can produce perfect images: spatial resolution is limited by the Rayleigh diffraction bound that is a consequence of the imager's finite spatial extent. We show some N-photon strategies that permit resolution of details that are smaller than this bound, attaining either a 1/sqrt(N) enhancement (standard quantum limit) or a 1/N enhancement (Heisenberg limit) over standard techniques. In the incoherent imaging regime, the methods presented are loss resistant, because they can be implemented with classical-state light sources. Our results may be of importance in many applications: microscopy, telescopy, lithography, metrology, etc.},
author = {Giovannetti, Vittorio and Lloyd, Seth and MacCone, Lorenzo and Shapiro, Jeffrey H.},
doi = {10.1103/PhysRevA.79.013827},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Giovannetti et al. - 2009 - Sub-Rayleigh-diffraction-bound quantum imaging.pdf:pdf},
isbn = {1050-2947},
issn = {10502947},
journal = {Physical Review A},
number = {1},
pages = {013827},
title = {{Sub-Rayleigh-diffraction-bound quantum imaging}},
volume = {79},
year = {2009}
}
@article{Zhang2013,
abstract = {The minimum error of unbiased parameter estimation is quantified by the quantum Fisher information in accordance to the Cram$\backslash$'{\{}e{\}}r-Rao bound. We indicate that only superposed NOON states by simultaneous measurements can achieve the maximum quantum Fisher information with form {\$}{\textless}\backslashhat{\{}N{\}}{\^{}}{\{}2{\}}{\textgreater}{\$} for a given photon number distribution by a POVM in linear two-path interferometer phase measurement. We present a series of specified superposed states with infinite quantum Fisher information but with finite average photon numbers. The advantage of this unbounded quantum Fisher information will be beneficial to many applications in quantum technology.},
author = {Zhang, Y. R. and Jin, G. R. and Cao, J. P. and Liu, W. M. and Fan, H.},
doi = {10.1088/1751-8113/46/3/035302},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Zhang et al. - 2013 - Unbounded quantum Fisher information in two-path interferometry with finite photon number.pdf:pdf},
issn = {17518113},
journal = {Journal of Physics A: Mathematical and Theoretical},
number = {3},
pages = {035302},
title = {{Unbounded quantum Fisher information in two-path interferometry with finite photon number}},
volume = {46},
year = {2013}
}
@article{Datta2011,
author = {Datta, Animesh and Zhang, Lijian and Thomas-peter, Nicholas and Dorner, Uwe and Smith, Brian J. and Walmsley, Ian A.},
doi = {10.1103/PhysRevA.83.063836},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Datta et al. - 2011 - Quantum metrology with imperfect states and detectors.pdf:pdf},
journal = {Physical Review A},
number = {6},
pages = {063836},
title = {{Quantum metrology with imperfect states and detectors}},
volume = {83},
year = {2011}
}
@article{Walther2004,
abstract = {Superposition is one of the most distinctive features of quantum theory and has been demonstrated in numerous single-particle interference experiments. Quantum entanglement, the coherent superposition of states in multi-particle systems, yields more complex phenomena. One important type of multi-particle experiment uses path-entangled number states, which exhibit pure higher-order interference and the potential for applications in metrology and imaging; these include quantum interferometry and spectroscopy with phase sensitivity at the Heisenberg limit, or quantum lithography beyond the classical diffraction limit. It has been generally understood that in optical implementations of such schemes, lower-order interference effects always decrease the overall performance at higher particle numbers. Such experiments have therefore been limited to two photons. Here we overcome this limitation, demonstrating a four-photon interferometer based on linear optics. We observe interference fringes with a periodicity of one-quarter of the single-photon wavelength, confirming the presence of a four-particle mode-entangled state. We anticipate that this scheme should be extendable to arbitrary photon numbers, holding promise for realizable applications with entanglement-enhanced performance.},
author = {Walther, Philip and Pan, Jian Wei and Aspelmeyer, Markus and Ursin, Rupert and Gasparoni, Sara and Zeilinger, Anton},
doi = {10.1038/nature02552},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Walther et al. - 2004 - De Broglie wavelength of a non-local four-photon state.pdf:pdf},
isbn = {0028-0836},
issn = {00280836},
journal = {Nature},
number = {6988},
pages = {158--161},
pmid = {15141205},
title = {{De Broglie wavelength of a non-local four-photon state}},
volume = {429},
year = {2004}
}
@article{Agarwal2001,
author = {Agarwal, Girish S. and Boyd, Robert W. and Nagasako, Elna M. and Bentley, Sean J.},
doi = {10.1103/PhysRevLett.86.1389},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Agarwal et al. - 2001 - Comment on “quantum interferometric optical lithography Exploiting entanglement to beat the diffraction limit”.pdf:pdf},
isbn = {1-55752-608-7},
issn = {10797114},
journal = {Physical Review Letters},
number = {7},
pages = {1389},
pmid = {10991220},
title = {{Comment on “quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit”}},
volume = {86},
year = {2001}
}
@article{Liu2016,
abstract = {We apply a generalized form of entangled coherent state (ECS) in an optical interferometer to detect the phase sensitivity. Both the linear and nonlinear protocols have been considered. We find that, similarly with the generalized NOON state [Phys. Rev. Lett. 111, 070403 (2013)], utilizing the simultaneous estimation, this generalized form of ECS gives a O(d) advantage on the parameter number d compared to the independent estimation, and the nonlinear protocol shows no advantage on d than the linear counterpart in these cases. Furthermore, this generalized form of ECS can give a lower Cramer-Rao bound than the generalized NOON state in both linear and nonlinear protocols. The homodyne detection has been applied in the linear protocol in the last.},
author = {Liu, Jing and Lu, Xiao Ming and Sun, Zhe and Wang, Xiaoguang},
doi = {10.1088/1751-8113/49/11/115302},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Liu et al. - 2016 - Quantum multiparameter metrology with generalized entangled coherent state.pdf:pdf},
isbn = {1751-8113},
issn = {17518121},
journal = {Journal of Physics A: Mathematical and Theoretical},
number = {11},
pages = {115302},
title = {{Quantum multiparameter metrology with generalized entangled coherent state}},
volume = {49},
year = {2016}
}
@article{Gong2017,
abstract = {We theoretically derive the lower and upper bounds of quantum Fisher information (QFI) of an SU(1,1) interferometer whatever the input state chosen. According to the QFI, the crucial resource for quantum enhancement is shown to be large intramode correlations indicated by the Mandel {\$}Q{\$}-parameter. For a photon-subtracted squeezed vacuum state with high super-Poissonian statistics in one input port and a coherent state in the other input port, the quantum Cram$\backslash$'{\{}e{\}}r-Rao bound of the SU(1,1) interferometer can beat {\$}1/\backslashlangle\backslashhat{\{}N{\}}\backslashrangle{\$} scaling in presence of large fluctuations in the number of photons, with a given fixed input mean number of photons. The definition of the Heisenberg limit (HL) should take into account the amount of fluctuations. The HL considering the number fluctuation effect may be the ultimate phase limit.},
author = {Gong, Qian Kun and Hu, Xiu Ling and Li, Dong and Yuan, Chun Hua and Ou, Z. Y. and Zhang, Weiping},
doi = {10.1103/PhysRevA.96.033809},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Gong et al. - 2017 - Intramode-correlation-enhanced phase sensitivities in an SU(1,1) interferometer.pdf:pdf},
issn = {24699934},
journal = {Physical Review A},
number = {3},
pages = {033809},
title = {{Intramode-correlation-enhanced phase sensitivities in an SU(1,1) interferometer}},
volume = {96},
year = {2017}
}
@article{Wang2016,
abstract = {By pulsed s-shell resonant excitation of a single quantum dot-micropillar system, we generate long streams of a thousand of near transform-limited single photons with high mutual indistinguishability. Hong-Ou-Mandel interference of two photons are measured as a function of their emission time separation varying from 13 ns to 14.7 {\{}$\backslash$mu{\}}s, where the visibility slightly drops from 95.9(2){\%} to a plateau of 92.1(5){\%} through a slow dephasing process occurring at time scale of 0.7 {\{}$\backslash$mu{\}}s. Temporal and spectral analysis reveal the pulsed resonance fluorescence single photons are close to transform limit, which are readily useful for multi-photon entanglement and interferometry experiments.},
author = {Wang, Hui and Duan, Z. C. and Li, Y. H. and Chen, Si and Li, J. P. and He, Y. M. and Chen, M. C. and He, Yu and Ding, X. and Peng, Cheng Zhi and Schneider, Christian and Kamp, Martin and H{\"{o}}fling, Sven and Lu, Chao Yang and Pan, Jian Wei},
doi = {10.1103/PhysRevLett.116.213601},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Wang et al. - 2016 - Near-transform-limited single photons from an efficient solid-state quantum emitter.pdf:pdf},
isbn = {0031-9007},
issn = {10797114},
journal = {Physical Review Letters},
number = {21},
pages = {213601},
pmid = {27284656},
title = {{Near-transform-limited single photons from an efficient solid-state quantum emitter}},
volume = {116},
year = {2016}
}
@article{Hofmann2007,
abstract = {We show that the quantum interference between down-converted photon$\backslash$npairs and photons from coherent$\backslash$n$\backslash$nlaser light can produce a maximally path entangled N-photon output$\backslash$ncomponent with a fidelity greater than$\backslash$n$\backslash$n90{\%} for arbitrarily high photon numbers. A simple beam splitter operation$\backslash$ncan thus transform the two-photon$\backslash$n$\backslash$ncoherence of down-converted light into an almost optimal N-photon$\backslash$ncoherence.},
author = {Hofmann, Holger F. and Ono, Takafumi},
doi = {10.1103/PhysRevA.76.031806},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Hofmann, Ono - 2007 - High-photon-number path entanglement in the interference of spontaneously down-converted photon pairs with coheren.pdf:pdf},
issn = {10502947},
journal = {Physical Review A},
number = {3},
pages = {031806},
title = {{High-photon-number path entanglement in the interference of spontaneously down-converted photon pairs with coherent laser light}},
volume = {76},
year = {2007}
}
@article{Sivakumar2015,
abstract = {{\textcopyright} 2015 Published by NRC Research Press.Mixing the squeezed vacuum and coherent state in a beam splitter generates NOON states of the electromagnetic field, but with fidelity less than unity. In this article it is shown that the output of the beam splitter generates the NOON states with unit fidelity if superposed coherent states are used instead of the squeezed vacuum. Also, the post-selection probability of NOON states is shown to be higher.},
author = {Sivakumar, S.},
doi = {10.1139/cjp-2014-0030},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Sivakumar - 2015 - Superposed coherent states improve fidelity of NOON states generated in post-selection.pdf:pdf},
issn = {00084204},
journal = {Canadian Journal of Physics},
keywords = {03.65.Ca,42.50.Dv,42.50.St},
number = {4},
pages = {373--376},
title = {{Superposed coherent states improve fidelity of NOON states generated in post-selection}},
volume = {93},
year = {2015}
}
@inproceedings{Zhang2017FiO,
address = {Washington D.C.},
author = {Zhang, Lu and Chan, Kam Wai Clifford},
booktitle = {Frontiers in Optics/Laser Science (FiO/LS)},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Zhang, Wai, Chan - 2017 - Generation of multi-mode NOON states with three photons using linear optics.pdf:pdf},
pages = {Paper JW4A.22},
title = {{Generation of multi-mode NOON states with three photons using linear optics}},
year = {2017}
}
@article{Divochiy2008,
abstract = {We demonstrate a photon-number-resolving (PNR) detector, based on parallel superconducting nanowires, capable of resolving up to 5 photons in the telecommunication wavelength range, with sensitivity and speed far exceeding existing approaches.},
author = {Divochiy, Aleksander and Et al},
doi = {10.1109/QELS.2008.4553065},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Divochiy, et al - 2008 - Superconducting nanowire photon number resolving detector at telecom wavelength.pdf:pdf},
isbn = {1557528594},
journal = {Nature Photonics},
number = {5},
pages = {302},
title = {{Superconducting nanowire photon number resolving detector at telecom wavelength}},
volume = {2},
year = {2008}
}
@article{Boto2000,
abstract = {Summary form only given. It has been known for some time that entangled photon pairs, such as generated by spontaneous parametric down conversion, have unusual imaging characteristics with sub-shot-noise interferometric phase measurement. In fact, Fonseca, et al., recently demonstrated resolution of a two-slit diffraction patterned at half the Rayleigh limit in a coincidence counting experiment. What we show is that this type of effect is possible not only in coincidence counting experiments, but also in real two-photon absorbing systems, such as those used in classical interferometric lithography. In particular, we will demonstrate that quantum entanglement is the resource that allows sub-diffraction limited lithography.},
author = {Boto, Agedi N. and Kok, Pieter and Abrams, Daniel S. and Braunstein, Samuel L.},
doi = {10.1109/QELS.2000.902023},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Wolfgramm, Cer{\`{e}}, Mitchell - 2002 - Generation of three-photon entangled state by quantum interference between a coherent state and pa(2).pdf:pdf},
isbn = {1-55752-608-7},
issn = {1094-5695},
journal = {Physical Review Letters},
number = {13},
pages = {2733--2736},
pmid = {10991220},
title = {{Quantum interferometric optical lithography: exploiting entanglement to beat the diffraction limit}},
volume = {85},
year = {2000}
}
@article{Nagata2007,
abstract = {Precision measurements are important across all fields of science. In particular, optical phase measurements can be used to measure distance, position, displacement, acceleration and optical path length. Quantum entanglement enables higher precision than would otherwise be possible. We demonstrate an optical phase measurement with an entangled four photon interference visibility greater than the threshold to beat the standard quantum limit--the limit attainable without entanglement. These results open the way for new high-precision measurement applications.},
author = {Nagata, Tomohisa and Okamoto, Ryo and O'Brien, Jeremy L. and Sasaki, Keiji and Takeuchi, Shigeki},
doi = {10.1126/science.1138007},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Nagata et al. - 2007 - Beating the Standard Quantum Limit with Four Entangled Photons.pdf:pdf},
isbn = {0036-8075},
issn = {1095-9203},
journal = {Science},
number = {5825},
pages = {726--729},
pmid = {17478715},
title = {{Beating the standard quantum limit with four-entangled photons}},
volume = {316},
year = {2007}
}
@article{Knott2016,
author = {Knott, P. A. and Proctor, T. J. and Hayes, A. J. and Ralph, J. F. and Kok, P. and Dunningham, J. A.},
doi = {10.1103/PhysRevA.94.062312},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Knott et al. - 2016 - Local versus global strategies in multiparameter estimation(2).pdf:pdf},
issn = {24699934},
journal = {Physical Review A},
number = {6},
pages = {062312},
title = {{Local versus global strategies in multiparameter estimation}},
volume = {94},
year = {2016}
}
@article{Giovannetti2011,
abstract = {In classical estimation theory, the central limit theorem implies that the statistical error in a measurement outcome can be reduced by an amount proportional to n{\^{}}(-1/2) by repeating the measures n times and then averaging. Using quantum effects, such as entanglement, it is often possible to do better, decreasing the error by an amount proportional to 1/n. Quantum metrology is the study of those quantum techniques that allow one to gain advantages over purely classical approaches. In this review, we analyze some of the most promising recent developments in this research field. Specifically, we deal with the developments of the theory and point out some of the new experiments. Then we look at one of the main new trends of the field, the analysis of how the theory must take into account the presence of noise and experimental imperfections.},
author = {Giovannetti, Vittorio and Lloyd, Seth and MacCone, Lorenzo},
doi = {10.1038/nphoton.2011.35},
file = {:C$\backslash$:/Users/1991l/Dropbox/2018 dissertation/reference papers/giovannetti2011{\_}advancedInQuantumMetrology.pdf:pdf},
isbn = {1749-4885},
issn = {17494885},
journal = {Nature Photonics},
number = {4},
pages = {222--229},
pmid = {15550661},
publisher = {Nature Publishing Group},
title = {{Advances in quantum metrology}},
volume = {5},
year = {2011}
}
@article{Kok2004,
abstract = {We explore the intimate relationship between quantum lithography,$\backslash$nHeisenberg-limited parameter estimation and the rate of dynamical$\backslash$nevolution of quantum states. We show how both the enhanced accuracy$\backslash$nin measurements and the increased resolution in quantum lithography$\backslash$nfollow from the use of entanglement. Mathematically, the hyper-resolution$\backslash$nof quantum lithography appears naturally in the derivation of Heisenberg-limited$\backslash$nparameter estimation. We also review recent experiments offering$\backslash$na proof of the principle of quantum lithography, and we address the$\backslash$nquestion of state preparation and the fabrication of suitable photoresists.},
author = {Kok, Pieter and Braunstein, Samuel L. and Dowling, Jonathan P.},
doi = {10.1088/1464-4266/6/8/029},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Kok, Braunstein, Dowling - 2004 - Quantum lithography, entanglement and Heisenberg-limited parameter estimation(2).pdf:pdf},
issn = {14644266},
journal = {Journal of Optics B: Quantum and Semiclassical Optics},
keywords = {Quantum imaging,Quantum metrology,Shot-noise,Standard quantum limit},
number = {8},
pages = {S811},
title = {{Quantum lithography, entanglement and Heisenberg-limited parameter estimation}},
volume = {6},
year = {2004}
}
@article{Shepard2016,
abstract = {Within the quantum phase representation we derive Heisenberg limits, in closed form, for N00N states and two other classes of states that can outperform these in terms of local performance metrics relevant for multiply-peaked distributions. One of these can also enhance the super-resolution factor beyond that of a N00N state of the same power, at the expense of diminished fringe visibility. An accurate phase estimation algorithm, which can be applied to the minimally resourced apparatus of a standard interferometer, is shown to be resilient to the presence of additive white-Gaussian noise.},
author = {Shepard, Scott Roger and Moxley, Frederick Ira III and Dowling, Jonathan P.},
doi = {10.1103/PhysRevA.93.033805},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Shepard, Moxley, Dowling - 2016 - Quantum phase representation of Heisenberg limits and a minimally resourced quantum phase estimator.pdf:pdf},
issn = {24699934},
journal = {Physical Review A},
number = {3},
pages = {033805},
title = {{Quantum phase representation of Heisenberg limits and a minimally resourced quantum phase estimator}},
volume = {93},
year = {2016}
}
@book{Nielsen2010,
abstract = {One of the most cited books in physics of all time, Quantum Computation and Quantum Information remains the best textbook in this exciting field of science. This 10th anniversary edition includes an introduction from the authors setting the work in context. This comprehensive textbook describes such remarkable effects as fast quantum algorithms, quantum teleportation, quantum cryptography and quantum error-correction. Quantum mechanics and computer science are introduced before moving on to describe what a quantum computer is, how it can be used to solve problems faster than 'classical' computers and its real-world implementation. It concludes with an in-depth treatment of quantum information. Containing a wealth of figures and exercises, this well-known textbook is ideal for courses on the subject, and will interest beginning graduate students and researchers in physics, computer science, mathematics, and electrical engineering.},
author = {Nielsen, Michael A. and Chuang, Isaac L.},
booktitle = {Cambridge University Press},
doi = {10.1017/CBO9780511976667},
isbn = {1107002176},
issn = {00029505},
keywords = {1107002176,Analytic Mechanics (Mathematical Aspects),Cambridge University Press,Computer Science,Computer Science (Specific Aspects),Computers - General Information,Computers / Computer Science,Isaac L. Chuang,Michael A. Nielsen,Physics,Physics - Quantum Theory,Quantum Computation and Quantum Information: 10th,Quantum computers,Quantum physics (quantum mechanics {\&} quantum field,Science,Science / Physics / Quantum Theory,Science/Mathematics},
pages = {702},
pmid = {11928608},
publisher = {Cambridge university press},
title = {{Quantum computation and quantum information}},
year = {2010}
}
@article{Mitchell2004,
abstract = {Interference phenomena are ubiquitous in physics, often forming the basis of demanding measurements. Examples include Ramsey interferometry in atomic spectroscopy, X-ray diffraction in crystallography and optical interferometry in gravitational-wave studies. It has been known for some time that the quantum property of entanglement can be exploited to perform super-sensitive measurements, for example in optical interferometry or atomic spectroscopy. The idea has been demonstrated for an entangled state of two photons, but for larger numbers of particles it is difficult to create the necessary multiparticle entangled states. Here we demonstrate experimentally a technique for producing a maximally entangled three-photon state from initially non-entangled photons. The method can in principle be applied to generate states of arbitrary photon number, giving arbitrarily large improvement in measurement resolution. The method of state construction requires non-unitary operations, which we perform using post-selected linear-optics techniques similar to those used for linear-optics quantum computing.},
author = {Mitchell, M. W. and Lundeen, J. S. and Steinberg, A. M.},
doi = {10.1038/nature02493},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Mitchell, Lundeen, Steinberg - 2004 - Super-resolving phase measurements with a multiphoton entangled state.pdf:pdf},
isbn = {0028-0836},
issn = {00280836},
journal = {Nature},
number = {6988},
pages = {161--164},
pmid = {15141206},
title = {{Super-resolving phase measurements with a multiphoton entangled state}},
volume = {429},
year = {2004}
}
@article{Pryde2003,
abstract = {We theoretically demonstrate a method for producing the maximally path-entangled state (1/2√)(|N,0⟩+exp[iN$\phi$]|0,N⟩) using intensity-symmetric multiport beam splitters, single photon inputs, and either photon-counting postselection or conditional measurement. The use of postselection enables successful implementation with non-unit efficiency detectors. We also demonstrate how to make the same state more conveniently by replacing one of the single photon inputs by a coherent state.},
author = {Pryde, G. J. and White, A. G.},
doi = {10.1103/PhysRevA.68.052315},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Pryde, White - 2003 - Creation of maximally entangled photon-number states using optical fiber multiports.pdf:pdf},
isbn = {1050-2947},
issn = {1050-2947},
journal = {Physical Review A},
number = {5},
pages = {052315},
title = {{Creation of maximally entangled photon-number states using optical fiber multiports}},
volume = {68},
year = {2003}
}
@article{Sanaka2006,
abstract = {Unprecedented optical nonlinearities can be generated probabilistically in simple linear-optical networks conditioned on specific measurement outcomes. We describe a highly controllable quantum filter for photon number states, which takes advantage of such a measurement-induced amplitude nonlinearity. The basis for this filter is multiphoton nonclassical interference which we demonstrate for one- and two-photon states over a wide range of beam splitter reflectivities. Specifically, we show that the transmission probability, conditional on a specific measurement outcome, can be larger for a two-photon state than a one-photon state; this is not possible with linear optics alone.},
author = {Sanaka, Kaoru and Resch, Kevin J. and Zeilinger, Anton},
doi = {10.1103/PhysRevLett.96.083601},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Sanaka, Resch, Zeilinger - 2006 - Filtering out photonic fock states.pdf:pdf},
isbn = {0031-9007},
issn = {00319007},
journal = {Physical Review Letters},
number = {8},
pages = {083601},
pmid = {16606178},
title = {{Filtering out photonic fock states}},
volume = {96},
year = {2006}
}
@article{Hong1986,
abstract = {In the process of spontaneous parametric down-conversion a signal and an idler photon are created simultaneously. By use of the photoelectric detection of the signal photon as a gate, a good approximation to the ideal localized one-photon state can be achieved. This has been confirmed by direct photon-counting measurements.},
author = {Hong, C. K. and Mandel, L.},
doi = {10.1103/PhysRevLett.56.58},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Hong, Mandel - 1986 - Experimental realization of a localized one-photon state.pdf:pdf},
isbn = {0031-9007},
issn = {00319007},
journal = {Physical Review Letters},
number = {1},
pages = {58},
pmid = {10032528},
title = {{Experimental realization of a localized one-photon state}},
volume = {56},
year = {1986}
}
@article{Gerry2001,
abstract = {When a quantum-optical Fredkin gate is embedded into a Mach-Zehnder interferometer, state reduction techniques permit the generation of maximally entangled states of the radiation field when Fock states are input to the device. These states exactly reach the Heisenberg limit of phase sensitivity. We investigate the consequences of injecting more general states, and particularly coherent states, into the apparatus. Applications to interferometry and photolithography are discussed.},
author = {Gerry, Christopher C. and Campos, R. A.},
doi = {10.1103/PhysRevA.64.063814},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Gerry, Campos - 2001 - Generation of maximally entangled photonic states with a quantum-optical Fredkin gate.pdf:pdf},
issn = {1050-2947},
journal = {Physical Review A},
number = {6},
pages = {063814},
title = {{Generation of maximally entangled photonic states with a quantum-optical Fredkin gate}},
volume = {64},
year = {2001}
}
@article{Paris2009,
abstract = {Several quantities of interest in quantum information, including entanglement and purity, are nonlinear functions of the density matrix and cannot, even in principle, correspond to proper quantum observables. Any method aimed to determine the value of these quantities should resort to indirect measurements and thus corresponds to a parameter estimation problem whose solution, i.e the determination of the most precise estimator, unavoidably involves an optimization procedure. We review local quantum estimation theory and present explicit formulas for the symmetric logarithmic derivative and the quantum Fisher information of relevant families of quantum states. Estimability of a parameter is defined in terms of the quantum signal-to-noise ratio and the number of measurements needed to achieve a given relative error. The connections between the optmization procedure and the geometry of quantum statistical models are discussed. Our analysis allows to quantify quantum noise in the measurements of non observable quantities and provides a tools for the characterization of signals and devices in quantum technology.},
author = {Paris, Matteo G. A.},
doi = {10.1142/S0219749909004839},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Paris - 2009 - Quantum estimation for quantum technology.pdf:pdf},
issn = {0219-7499},
journal = {International Journal of Quantum Information},
pages = {125--137},
title = {{Quantum estimation for quantum technology}},
volume = {7},
year = {2009}
}
@article{Fiurasek2002,
author = {Fiur{\'{a}}{\v{s}}ek, Jarom{\'{i}}r},
doi = {10.1103/PhysRevA.65.053818},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Fiur{\'{a}}{\v{s}}ek - 2002 - Conditional generation of iNi -photon entangled states of light.pdf:pdf},
issn = {1050-2947},
journal = {Physical Review A},
number = {5},
pages = {053818},
title = {{Conditional generation of N -photon entangled states of light}},
volume = {65},
year = {2002}
}
@article{Kok2011,
abstract = {Optical noon states (|N,0{\textgreater} + |0,N{\textgreater}) are an important resource for Heisenberg-limited metrology and quantum lithography. The only known methods for creating noon states with arbitrary {\$}N{\$} via linear optics and projective measurments seem to have a limited range of application due to imperfect phase control. Here, we show that bootstrapping techniques can be used to create high-fidelity noon states of arbitrary size.},
author = {Kok, Pieter},
doi = {10.1134/S0030400X11110178},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Wolfgramm, Cer{\`{e}}, Mitchell - 2002 - Generation of three-photon entangled state by quantum interference between a coherent state and pa(3).pdf:pdf},
issn = {0030-400X},
journal = {Optics and Spectroscopy},
number = {4},
pages = {520--522},
title = {{Creating large NOON states with imperfect phase control}},
volume = {111},
year = {2011}
}
@article{Crespi2012,
abstract = {Optical interferometry is amongst the most sensitive techniques for precision measurement. By increasing the light intensity a more precise measurement can usually be made. However, in some applications the sample is light sensitive. By using entangled states of light the same precision can be achieved with less exposure of the sample. This concept has been demonstrated in measurements of fixed, known optical components. Here we use two-photon entangled states to measure the concentration of the blood protein bovine serum albumin (BSA) in an aqueous buffer solution. We use an opto-fluidic device that couples a waveguide interferometer with a microfluidic channel. These results point the way to practical applications of quantum metrology to light sensitive samples.},
author = {Crespi, Andrea and Lobino, Mirko and Matthews, Jonathan C. F. and Politi, Alberto and Neal, Chris R. and Ramponi, Roberta and Osellame, Roberto and O'Brien, Jeremy L.},
doi = {10.1063/1.4724105},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Crespi et al. - 2012 - Measuring protein concentration with entangled photons(3).pdf:pdf},
isbn = {00036951},
issn = {00036951},
journal = {Applied Physics Letters},
number = {23},
pages = {233704},
title = {{Measuring protein concentration with entangled photons}},
volume = {100},
year = {2012}
}
@article{Ciampini2016,
abstract = {Quantum metrology is the state-of-the-art measurement technology. It uses quantum resources to enhance the sensitivity of phase estimation beyond what reachable within classical physics. While single parameter estimation theory has been widely investigated, much less is known about the simultaneous estimation of multiple phases, which finds key applications in imaging and sensing. In this manuscript we provide conditions of useful entanglement (among multimode particles, qudits) for multiphase estimation and adapt them to multiarm Mach-Zehnder interferometry. We discuss benchmark multimode Fock states containing useful qudit entanglement and overcoming the sensitivity of separable qudit states in three and four arm Mach-Zehnder-like interferometers - currently within the reach of integrated photonics technology.},
author = {Ciampini, Mario A. and Spagnolo, Nicol{\`{o}} and Vitelli, Chiara and Pezz{\`{e}}, Luca and Smerzi, Augusto and Sciarrino, Fabio},
doi = {10.1038/srep28881},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Ciampini et al. - 2016 - Quantum-enhanced multiparameter estimation in multiarm interferometers.pdf:pdf},
issn = {20452322},
journal = {Scientific Reports},
pages = {28881},
title = {{Quantum-enhanced multiparameter estimation in multiarm interferometers}},
volume = {6},
year = {2016}
}
@article{Szczykulska2016,
abstract = {The simultaneous quantum estimation of multiple parameters can provide a better precision than estimating them individually. This is an effect that is impossible classically. We review the rich background of multi-parameter quantum metrology, some of the main results in the field and its recent advances. We close by highlighting future challenges and open questions.},
author = {Szczykulska, Magdalena and Baumgratz, Tillmann and Datta, Animesh},
doi = {10.1080/23746149.2016.1230476},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Szczykulska, Baumgratz, Datta - 2016 - Multi-parameter Quantum Metrology.pdf:pdf},
issn = {2374-6149},
journal = {Advances in Physics: X},
number = {4},
pages = {621--639},
title = {{Multi-parameter quantum metrology}},
volume = {1},
year = {2016}
}
@article{Reimer2012,
abstract = {The ability to achieve near-unity light-extraction efficiency is necessary for a truly deterministic single-photon source. The most promising method to reach such high efficiencies is based on embedding single-photon emitters in tapered photonic waveguides defined by top-down etching techniques. However, light-extraction efficiencies in current top-down approaches are limited by fabrication imperfections and etching-induced defects. The efficiency is further tempered by randomly positioned off-axis quantum emitters. Here we present perfectly positioned single quantum dots on the axis of a tailored nanowire waveguide using bottom-up growth. In comparison to quantum dots in nanowires without waveguides, we demonstrate a 24-fold enhancement in the single-photon flux, corresponding to a light-extraction efficiency of 42{\%}. Such high efficiencies in one-dimensional nanowires are promising to transfer quantum information over large distances between remote stationary qubits using flying qubits within the same nanowire p-n junction.},
author = {Reimer, Michael E. and Bulgarini, Gabriele and Akopian, Nika and Hocevar, Mo{\"{i}}ra and Bavinck, Maaike Bouwes and Verheijen, Marcel A. and Bakkers, Erik P A M and Kouwenhoven, Leo P. and Zwiller, Val},
doi = {10.1038/ncomms1746},
file = {:C$\backslash$:/Users/1991l/Dropbox/2018 dissertation/reference papers/others/single photon generation/ncomms1746{\_}Reimer2012{\_}quantumdot.pdf:pdf},
isbn = {20411723},
issn = {20411723},
journal = {Nature Communications},
pages = {737},
pmid = {22415828},
title = {{Bright single-photon sources in bottom-up tailored nanowires}},
volume = {3},
year = {2012}
}
@article{Campos2003,
abstract = {Holland and Burnett Phys. Rev. Lett. 71, 1355 1993 have argued that twin Fock states of equal photon number N injected at both input ports of a Mach-Zehnder interferometer lead to phase measurements with accuracies approaching the Heisenberg limit  HL1/(2N). However, the method of phase detection sug- gested by those authors, obtaining the difference of the photocurrents at the output ports of the interferometer, is not sensitive to the phase difference between the two interferometer paths; in fact, the photocurrent vanishes. In this paper we show that the use of parity measurements on just one of the output modes not only is sensitive to the phase difference but that the sensitivity approaches the Heisenberg limit for large N.},
author = {Campos, R. A. and Gerry, Christopher C. and Benmoussa, A.},
doi = {10.1103/PhysRevA.68.023810},
file = {:C$\backslash$:/Users/1991l/AppData/Local/Mendeley Ltd./Mendeley Desktop/Downloaded/Campos, Gerry, Benmoussa - 2003 - Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements.pdf:pdf},
issn = {1050-2947},
journal = {Physical Review A},
number = {2},
pages = {023810},
title = {{Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements}},
volume = {68},
year = {2003}
}
