\contentsline {chapter}{Acknowledgements}{iv}{chapter*.1}
\contentsline {chapter}{List of Tables}{viii}{chapter*.3}
\contentsline {chapter}{List of Figures}{ix}{chapter*.4}
\contentsline {chapter}{List of Abbreviations}{xi}{chapter*.5}
\contentsline {chapter}{Abstract}{xiii}{chapter*.6}
\contentsline {chapter}{\numberline {1}Introduction}{1}{chapter.1}
\contentsline {section}{\numberline {1.1}Motivation}{1}{section.1.1}
\contentsline {section}{\numberline {1.2}Quantization of electromagnetic field}{6}{section.1.2}
\contentsline {section}{\numberline {1.3}Basic states of light}{8}{section.1.3}
\contentsline {subsection}{\numberline {1.3.1}Fock state}{9}{subsection.1.3.1}
\contentsline {subsection}{\numberline {1.3.2}Coherent state}{11}{subsection.1.3.2}
\contentsline {subsection}{\numberline {1.3.3}Squeezed state}{13}{subsection.1.3.3}
\contentsline {subsection}{\numberline {1.3.4}NOON state}{17}{subsection.1.3.4}
\contentsline {section}{\numberline {1.4}Basic optical devices}{18}{section.1.4}
\contentsline {section}{\numberline {1.5}Measurement methods: pre-selection and post-selection}{24}{section.1.5}
\contentsline {chapter}{\numberline {2}Applications of NOON states in quantum metrology and quantum imaging}{26}{chapter.2}
\contentsline {section}{\numberline {2.1}Super-resolving measurement using two-mode NOON states}{28}{section.2.1}
\contentsline {subsection}{\numberline {2.1.1}Quantum lithography scheme}{28}{subsection.2.1.1}
\contentsline {subsection}{\numberline {2.1.2}Optical centroid measurement scheme}{31}{subsection.2.1.2}
\contentsline {section}{\numberline {2.2}Super-sensitive imaging using NOON states}{34}{section.2.2}
\contentsline {subsection}{\numberline {2.2.1}Single phase estimation using two-mode NOON states}{34}{subsection.2.2.1}
\contentsline {subsubsection}{Standard quantum limit}{34}{subsection.2.2.1}
\contentsline {subsubsection}{Heisenberg limit}{37}{equation.2.2.6}
\contentsline {subsection}{\numberline {2.2.2}Simultaneous multiple phase estimation using multi-mode NOON states\nobreakspace {}\cite {Zhang2017}}{40}{subsection.2.2.2}
\contentsline {section}{\numberline {2.3}Summary}{52}{section.2.3}
\contentsline {chapter}{\numberline {3}Generation of two-mode NOON states}{53}{chapter.3}
\contentsline {section}{\numberline {3.1}Method using cross-Kerr nonlinearity}{53}{section.3.1}
\contentsline {section}{\numberline {3.2}NOON state projective measurement}{56}{section.3.2}
\contentsline {section}{\numberline {3.3}Method using dual-Fock states}{57}{section.3.3}
\contentsline {section}{\numberline {3.4}Method using two-mode $N$-photon input}{60}{section.3.4}
\contentsline {section}{\numberline {3.5}Method of mixing coherent state with squeezed vacuum state}{62}{section.3.5}
\contentsline {section}{\numberline {3.6}Summary}{64}{section.3.6}
\contentsline {chapter}{\numberline {4}Generation of multi-mode NOON states}{65}{chapter.4}
\contentsline {section}{\numberline {4.1}Method using cross-Kerr nonlinearity\nobreakspace {}\cite {Zhang2017a}}{65}{section.4.1}
\contentsline {section}{\numberline {4.2}Method using $d$ $N$-photon Fock states\nobreakspace {}\cite {Zhang2017a}}{69}{section.4.2}
\contentsline {section}{\numberline {4.3}Methods using Fock state filters and fixed-photon-number states}{72}{section.4.3}
\contentsline {subsection}{\numberline {4.3.1}Generation using an evenly-distributed $N$-photon state\nobreakspace {}\cite {Zhang2017a}}{72}{subsection.4.3.1}
\contentsline {subsection}{\numberline {4.3.2}Generation of 4-photon NOON state using single photons}{76}{subsection.4.3.2}
\contentsline {section}{\numberline {4.4}Methods using FSF and nondeterministic-photon-number states}{79}{section.4.4}
\contentsline {subsection}{\numberline {4.4.1}Generation using $d$ coherent states\nobreakspace {}\cite {Zhang2017a}}{81}{subsection.4.4.1}
\contentsline {subsection}{\numberline {4.4.2}Generation using $d$ single-mode squeezed vacuum states\nobreakspace {}\cite {Zhang2018}}{84}{subsection.4.4.2}
\contentsline {subsection}{\numberline {4.4.3}Generation using one two-mode squeezed vacuum state\nobreakspace {}\cite {Zhang2018}}{86}{subsection.4.4.3}
\contentsline {section}{\numberline {4.5}Comparisons and summary}{88}{section.4.5}
\contentsline {chapter}{\numberline {5}Conclusion and future work}{92}{chapter.5}
\contentsline {section}{\numberline {5.1}Conclusion}{92}{section.5.1}
\contentsline {section}{\numberline {5.2}Future work}{94}{section.5.2}
\contentsline {chapter}{References}{95}{chapter*.30}
\contentsline {chapter}{Appendices}{103}{section*.31}
\contentsline {chapter}{\numberline {A}Universal optimal measure for the polarization estimation of light with arbitrary photon statistics\nobreakspace {}\cite {Zhang2016}}{104}{Appendix.1.A}
\contentsline {chapter}{\numberline {B}Proof of Eq.\nobreakspace {}(\ref {Eq:C0_Kok}) using mathematical induction}{110}{Appendix.1.B}
