稿本 / 論文(碩士)--香港中文大學硏究院哲學部,1992. / 參考文獻: leaves 131-134 / 李一帆. / 引論 --- p.i / Chapter 第I章 --- 量子力學的哥本哈根詮釋 / Chapter §1.1 --- 概述 --- p.1 / Chapter §1.2 --- 動力學 --- p.3 / Chapter §1.3 --- 波粒二象性與互補原理 --- p.6 / Chapter §1.4 --- 概率解釋 --- p.10 / Chapter §1.5 --- 波包約化 --- p.13 / Chapter §1.6 --- 測不準原理 --- p.16 / Chapter §1.7 --- 隱變量的不可能性 --- p.21 / Chapter § 1.8 --- Schrodinger的貓 --- p.24 / Chapter §1.9 --- EPR之謎 --- p.27 / Chapter 第II章 --- Popper對量子力學的重新解釋 / Chapter §2.1 --- 概述 --- p.31 / Chapter §2.2 --- 理解危機 --- p.35 / Chapter §2.21 --- 主觀主義 --- p.36 / Chapter §2.22 --- 工具論 --- p.3 / Chapter §2.3 --- 概率的傾向解釋 --- p.41 / Chapter §2.31 --- 統計性的量子論 --- p.41 / Chapter §2.32 --- 概率就是傾向 --- p.42 / Chapter §2.33 --- 傾向是實在的物理性質 --- p.45 / Chapter §2.4 --- 「波包約化」是概率現象 --- p.48 / Chapter §2.5 --- 只有「波」、「粒」二象 --- p.52 / Chapter §2.51 --- 「波粒二象性」與「常態人」 --- p.53 / Chapter §2.52 --- 再論「雙狹縫實驗」 --- p.54 / Chapter §2.6 --- 測不準關係的統計解釋 --- p.56 / Chapter §2.61 --- 散離關係 --- p.57 / Chapter §2.62 --- 「測量」與「預測」 --- p.60 / Chapter §2.63 --- 過去的測量 --- p.63 / Chapter §2.64 --- 一個不對稱的論証 --- p.65 / Chapter §2.65 --- 一個決定性的論証 --- p.66 / Chapter §2.7 --- 宇宙論 --- p.68 / Chapter §2.71 --- 量子論的世界圖像 --- p.69 / Chapter §2.72 --- 研究網領 --- p.73 / Chapter 第III章 --- 評Popper對量子論的詮釋 / Chapter §3.1 --- 概述 --- p.78 / Chapter §3.2 --- 「不確定性」與「散離關係」 --- p.79 / Chapter §3.21 --- 屹立不倒的「不確定性」 --- p.80 / Chapter §3.22 --- 散離關係的謬誤 --- p.88 / Chapter §3.3 --- 與「傾向」道別 --- p.95 / Chapter §3.31 --- 沒有「傾向」的量子論 --- p.96 / Chapter §3.32 --- 等價描述 --- p.101 / Chapter §3.33 --- 並非物理性質 --- p.106 / Chapter §3.34 --- 空洞的「硏究綱領」 --- p.109 / Chapter 附錄 --- 量子論的誕生及初步發展 --- p.113 / 註釋 --- p.123 / 參考書目 --- p.131

Chan Chung Ning. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1999. / Includes bibliographical references (leaves [86]-88). / Text in English; abstracts in English and Chinese. / Chan Chung Ning. / Abstract --- p.i / Abstract in Chinese --- p.ii / Acknowledgement --- p.iii / Contents --- p.iv / List of Figures --- p.vii / List of Tables --- p.xi / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Classical chaos and quantum chaos --- p.1 / Chapter 1.2 --- Motivations --- p.2 / Chapter 1.3 --- Structure of our study --- p.3 / Chapter Chapter 2. --- Integrability of Hamiltonian Systems --- p.5 / Chapter 2.1 --- Integrable systems --- p.5 / Chapter 2.2 --- KAM perturbation and Poincare surface section --- p.8 / Chapter 2.3 --- Surface sections of Robnik Billiards --- p.11 / Chapter 2.4 --- Linking classical and quantum chaos --- p.16 / Chapter Chapter 3. --- Constraint Operator Method --- p.18 / Chapter 3.1 --- Two-dimensional billiards --- p.18 / Chapter 3.2 --- Formalism of the constraint operator method with the Dirichlet boundary conditions --- p.19 / Chapter 3.3 --- Numerical results: eigenvalues of billiards --- p.24 / Chapter 3.4 --- Discussion on the constraint operator method --- p.29 / Chapter Chapter 4. --- The COM with the Neumann Boundary Conditions --- p.32 / Chapter 4.1 --- Formalism --- p.32 / Chapter 4.2 --- Numerical results --- p.35 / Chapter 4.3 --- Discussion --- p.38 / Chapter Chapter 5. --- Boundary Integral Method --- p.40 / Chapter 5.1 --- Introduction --- p.40 / Chapter 5.2 --- Berry's formalism --- p.41 / Chapter 5.3 --- A modified formalism --- p.46 / Chapter 5.4 --- Numerical results --- p.47 / Chapter 5.5 --- Discussion on the BIM --- p.53 / Chapter Chapter 6. --- Further Discussions on the BIM --- p.55 / Chapter 6.1 --- The choice of the Green's function --- p.55 / Chapter 6.2 --- Principal value --- p.58 / Chapter Chapter 7. --- Conformal Mapping Method --- p.64 / Chapter 7.1 --- Formalism --- p.64 / Chapter 7.2 --- Numerical results --- p.69 / Chapter 7.3 --- Summary --- p.73 / Chapter Chapter 8. --- Spectral Statistics --- p.76 / Chapter 8.1 --- Introduction --- p.76 / Chapter 8.2 --- Numerical results --- p.78 / Chapter 8.3 --- Summary --- p.80 / Chapter Chapter 9. --- Conclusion --- p.83 / Bibliography --- p.86

Fung Ho Tak. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 107-110). / Text in English; abstracts in English and Chinese. / Fung Ho Tak. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Introduction to Geometric phase --- p.1 / Chapter 1.2 --- Introduction to Bose Einstein Condensation --- p.3 / Chapter 1.3 --- Motivation --- p.4 / Chapter 2 --- Review on Geometric phase --- p.6 / Chapter 2.1 --- Geometric phase achieved by undergoing adiabatic cyclic evolution --- p.7 / Chapter 2.2 --- Geometric phase acquired by undergoing cyclic evolution --- p.10 / Chapter 2.3 --- Geometric phase acquired by undergoing any evolution --- p.13 / Chapter 2.4 --- Geometrical representation of a two-level system --- p.15 / Chapter 3 --- Geometric Phase in Physical Systems --- p.17 / Chapter 3.1 --- Aharonov-Bohm Effect --- p.18 / Chapter 3.2 --- An Electron in a Magnetic Field --- p.20 / Chapter 3.2.1 --- The geometric phase β0(t) --- p.23 / Chapter 3.2.2 --- The geometric phase β1(t) --- p.28 / Chapter 3.3 --- Geometrical picture of the two-level quantum system --- p.32 / Chapter 3.3.1 --- Geometrical interpretation of β0(t) --- p.33 / Chapter 3.3.2 --- Geometrical interpretation of β1(t) --- p.36 / Chapter 3.4 --- Summary --- p.37 / Chapter 4 --- Geometric phase of a particle in a vibrating cavity --- p.39 / Chapter 4.1 --- Energy of a particle in a vibrating spherical cavity --- p.40 / Chapter 4.2 --- Geometric phase of a particle in a vibrating spherical cavity --- p.43 / Chapter 4.2.1 --- β0(t) of a particle in a vibrating cavity --- p.44 / Chapter 4.2.2 --- β1(t) of a particle in a vibrating cavity --- p.46 / Chapter 4.3 --- The Rotating-Wave Approximation approach --- p.46 / Chapter 4.3.1 --- Energy of the particle by using RWA --- p.49 / Chapter 4.3.2 --- Geometric phase of the particle by RWA --- p.50 / Chapter 4.4 --- The SU(2) Method --- p.52 / Chapter 4.5 --- Summary --- p.53 / Chapter 5 --- Review on Bose Einstein Condensation --- p.55 / Chapter 6 --- Energies and wavefunctions of a condensate --- p.63 / Chapter 6.1 --- perturbation approach to solve the nonlinear Schrodinger equation --- p.63 / Chapter 6.2 --- Energy of a BEC in an oscillating harmonic trap --- p.66 / Chapter 6.3 --- Wavefunction of the condensate in a vibrating harmonic trap --- p.72 / Chapter 6.4 --- Energies and wavefunctions of SHO --- p.76 / Chapter 6.5 --- Summary --- p.78 / Chapter 7 --- "(δr)2,(δpr)2 and geometric phase of a condensate" --- p.79 / Chapter 7.1 --- Uncertainties in position and momentum --- p.80 / Chapter 7.1.1 --- (δr)2 and (δpr)2 for a BEC in an oscillating trap --- p.80 / Chapter 7.1.2 --- (δr) and (δpr) in a oscillating SHO --- p.85 / Chapter 7.2 --- Geometric phase of BEC --- p.85 / Chapter 7.2.1 --- β0(t) of BEC --- p.87 / Chapter 7.2.2 --- β1(t)of BEC --- p.90 / Chapter 7.3 --- Summary --- p.92 / Chapter 8 --- Summary --- p.95 / Chapter A --- Parameter space and Berry's phase for degenerate Hamilto- nian --- p.99 / Chapter B --- Dirac Phase Factor --- p.101 / Chapter C --- Hamiltonian of a frequency-varying harmonics oscillator --- p.104 / Bibliography --- p.107

One of the key distinctions between classical and quantum information is given by the no-cloning theorem: unlike bits, arbitrary qubits cannot be perfectly copied. This fact has been the inspiration for many quantum cryptographic protocols. In this thesis, we introduce a new cryptographic functionality called uncloneable encryption. This functionality allows the encryption of a classical message such that two collaborating but non-communicating adversaries may not both simultaneously recover the message, even when the encryption key is revealed. We achieve this functionality by using Wiesner’s conjugate coding scheme to encrypt the message. We show that the adversaries cannot both obtain all the necessary information for the correct decryption with high probability. Quantum-secure pseudorandom functions, modelled as random oracles, are then used to ensure that any partial information that the adversaries obtain does not give them an advantage in recovering the message.

Song Junliang = 帶有環交換作用的自旋1/2梯子模型中的量子纠缠 / 宋均亮. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 60-67). / Text in English; abstracts in English and Chinese. / Song Junliang = Dai you huan jiao huan zuo yong de zi xuan 1/2 ti zi mo xing zhong de liang zi jiu chan / Song Junliang. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- What is Entanglement --- p.1 / Chapter 1.2 --- Quantum Information and Entanglement --- p.4 / Chapter 1.3 --- Entanglement in Condensed Matter Physics --- p.6 / Chapter 1.4 --- The S = 1/2 Spin Ladder with Ring Exchange --- p.9 / Chapter 1.5 --- Arrangement of the Thesis Writing --- p.11 / Chapter 2 --- Measures of Entanglement --- p.13 / Chapter 2.1 --- Axiomatic Approach --- p.14 / Chapter 2.2 --- Entropy of entanglement in pure states --- p.16 / Chapter 2.3 --- Concurrence --- p.17 / Chapter 2.4 --- Negativity --- p.19 / Chapter 2.5 --- Other measurements --- p.20 / Chapter 3 --- Entanglement in S=l/2 Ladder with Ring Exchange at T=0 --- p.22 / Chapter 3.1 --- Model Hamiltonian and Phase Diagram --- p.22 / Chapter 3.2 --- Ground-state concurrence --- p.24 / Chapter 3.3 --- Two-site entanglement of the rung and the SU(4) point --- p.29 / Chapter 3.4 --- Scaling behavior of the block-block entanglement --- p.34 / Chapter 3.5 --- Entanglement of the Ferromagnetic state --- p.37 / Chapter 3.6 --- Other Measurements --- p.42 / Chapter 3.7 --- Summary and Discussion --- p.43 / Chapter 4 --- Thermal Entanglement --- p.45 / Chapter 4.1 --- A Four-Spin Plaquette --- p.46 / Chapter 4.2 --- Thermal concurrence --- p.50 / Chapter 4.3 --- Magnetic susceptibility as Entanglement Witness --- p.52 / Chapter 4.4 --- Numerical results in a 6 x 2 ladder --- p.54 / Chapter 4.5 --- Summary and Discussion --- p.55 / Chapter 5 --- Conclusion and future work --- p.58 / Bibliography --- p.60

當一個宏觀量子系統的基態因為一個參數的變動產生劇烈的變化時，量子臨界現象會伴隨出現。量子臨界現像是指示新物理產生的重要標誌。在傳統觀測方法裡，量子臨界現像只有在零溫或者低溫下才能被觀測到(這裡低溫是相對於系統中相互作用強度而言的)。我們發現，一個量子探針，如果它的相干時間足夠長，在高溫下依然可以探測到量子臨界現象。特別是，自旋回波可以移除熱漲落效應，從而揭示量子漲落中的臨界現象，而無需把系統冷卻到極低溫度。我們先採用一個嚴格可解模型，即一維橫場伊辛模型演示了在高溫下通過自旋回波揭示量子臨界現象的可能性。臨界行為可以通過嚴格解計算來研究，並可用噪音譜高斯近似法加以理解。通過對噪音譜的分析，我們發現，為觀測到量子臨界現象，傳統方法中所需的溫度(TQc )和探針退相干測量中所需的相干時間( tQc)存在對應關係， 即TQc~ l/tQc 並遠小於系統的相互作用強度。例如，有毫秒或者秒量級相干時間的探針可以用來探測到原本在10 ⁻⁹ K或者1O⁻¹² K溫度下才能看到的量子臨界現象而無需降低系統的溫度。這個發現提供了一種新的研究量子物質的方法。 / 我們還發明了一個用法拉第旋轉回波譜(FRES) 研究透明材料中的自旋噪音的方案，是一種關於測量法拉第旋轉魚漲落的方法。FRES通過抑制熱漲落展現高溫下的量子漲落。它使用的原理和核磁共振中的自旋回波類似。我們用一種稀土化合物LiHoF₄測試了我們的理論。FRES得到的量子漲落在相界上有一個增強的效應。FRES可以被推廣到更複雜的配置，對應核磁共振以及電子自旋共振中的更複雜的動力學去耦操控。以此，我們可以得到更多磁性材料的結構和動力學性質方面的信息。 / Quantum criticality occurs when the ground state of a macroscopic quantum system changes abruptly with tuning a system parameter. It is an important indicator of new quantum matters emerging. In conventional methods, quantum criticality is observable only at zero or low temperature (as compared with the interaction strength in the system). We find that a quantum probe, if its coherence time is long, can detect quantum criticality of a system at high temperature. In particular, the echo control over a spin probe can remove the thermal fluctuation effects and hence reveal the critical quantum fluctuation without requiring low temperature. We first use the exact solution of the one-dimensional transverse-field Ising model to demonstrate the possibility of detecting the quantum criticality at high temperature by spin echo. The critical behaviors have been calculated using the exact solution and understood with the noise spectrum analysis in the Gaussian noise approximation. Using the noise spectrum analysis, we establish the correspondence between the necessary low temperature (TQC) in conventional methods and the necessary long coherence time (tQC) in probe decoherence measurement to observe the quantum criticality, that is, TQC ~ 1/tQC and much less than the interaction strength of the system. For example, probes with quantum coherence time of milliseconds or seconds can be used to study, without cooling the system, quantum criticality that is previously known only observable at extremely low temperatures of nano- or pico-Kelvin. This finding provides a new possibility to study quantum matters. / We also designed a scheme of Faraday rotation echo spectroscopy (FRES) that can be used to study spin noise dynamics in transparent materials by measuring the fluctuation of Faraday rotation angles. The FRES suppresses the static part of the noise and reveal the quantum fluctuations at relatively high temperature, which shares the same idea of the spin echo technique in nuclear magnetic resonance (NMR). We tested our theory on a rare-earth compound LiHoF₄.The quantum fluctuation obtained by FRES gives an enhanced feature at the phase boundary. The FRES can be straightforwardly generalized to more complicated configurations that correspond to more complex dynamical decoupling sequences in NMR and electron spin resonance, which may give us more extensive information on the structural and dynamical properties of magnetic materials. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Chen, Shaowen = 自旋回波中的高溫量子臨界現象 / 陳少文. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. / Includes bibliographical references (leaves 73-80). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts also in Chinese. / Chen, Shaowen = Zi xuan hui bo zhong de gao wen liang zi lin jie xian xiang / Chen Shaowen. / Abstract --- p.1 / 摘要 --- p.3 / Acknowledgment --- p.4 / Chapter 1 --- Introduction --- p.5 / Chapter 1.1 --- Motivation --- p.5 / Chapter 1.2 --- Thesis outline --- p.9 / Chapter 2 --- Central Spin Decoherence Problem --- p.11 / Chapter 2.1 --- Introduction --- p.11 / Chapter 2.2 --- Spin Echo --- p.14 / Chapter 2.3 --- Noise spectrumapproach --- p.14 / Chapter 3 --- Criticality in One-dimensional Transverse Field Ising Model --- p.17 / Chapter 3.1 --- Introduction --- p.17 / Chapter 3.2 --- TheModel and the Exact Solution --- p.19 / Chapter 3.3 --- Results fromexact solution --- p.22 / Chapter 3.4 --- Noise spectrumapproach --- p.23 / Chapter 3.5 --- Time-inverse temperature correspondence --- p.24 / Chapter 3.6 --- Critical exponents --- p.26 / Chapter 3.7 --- More Discussions --- p.30 / Chapter 3.7.1 --- Noise spectra --- p.30 / Chapter 3.7.2 --- Finite probe-bath coupling effect --- p.30 / Chapter 3.7.3 --- Revivals in FID --- p.31 / Chapter 3.8 --- Perspectives for experimental observation --- p.32 / Chapter 3.9 --- Summary --- p.33 / Chapter 4 --- Faraday Roation Echo Spectroscopy --- p.39 / Chapter 4.1 --- Introduction --- p.39 / Chapter 4.2 --- Faraday rotation --- p.41 / Chapter 4.3 --- Faraday rotation echo --- p.44 / Chapter 5 --- Faraday rotation echo of lithium holmium tetrafluoride --- p.47 / Chapter 5.1 --- Introduction --- p.47 / Chapter 5.2 --- Lithium Holmium tetrafluoride: LiHoF₄ --- p.48 / Chapter 5.3 --- Faraday rotation echo spectroscopy --- p.52 / Chapter 5.4 --- Summary --- p.54 / Chapter 6 --- Conclusion and Future work --- p.55 / Chapter Appendix --- p.57 / Chapter A. --- Exact solution of 1D Transverse-field Isingmodel --- p.57 / Chapter B. --- Calculation of the magnetic susceptibility --- p.64 / Chapter C. --- Faraday Rotation --- p.66 / Bibliography --- p.73

Wang Hui. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 78-84). / Abstracts in English and Chinese. / ABSTRACT (ENGLISH) --- p.i / ABSTRACT (CHINESE) --- p.iii / ACKNOWLEDGEMENTS --- p.iv / CONTENTS --- p.v / Chapter CHAPTER 1: --- INTRODUCTION --- p.1 / Chapter 1.1 --- Motivation behind This Study --- p.1 / Chapter 1.2 --- Concept of Quantum Dots --- p.2 / Chapter 1.2.1 --- Introduction to Semiconductors / Chapter 1.2.2 --- From Bulk Semiconductor to Quantum Dots / Chapter 1.3 --- Device Applications of Quantum Dots --- p.10 / Chapter 1.3.1 --- Laser Diodes / Chapter 1.3.2 --- Infrared Photodetectors / Chapter CHAPTER 2: --- METAL-ORGANIC VAPOR PHASE EPITAXY --- p.14 / Chapter 2.1 --- Introduction in Epitaxial Growth --- p.14 / Chapter 2.1.1 --- What's Epitaxy / Chapter 2.1.2 --- Heteroepitaxy Techniques / Chapter 2.2 --- MOVPE Growth System and Principles --- p.15 / Chapter 2.2.1 --- What's MOVPE / Chapter 2.2.2 --- MOVPE Chemistry and Basic Concepts / Chapter 2.2.3 --- Growth Regimes in MOVPE Process / Chapter CHAPTER 3: --- SELF-ASSEMBLED QUANTUM DOT GROWTH THEORY --- p.23 / Chapter 3.1 --- Strained Layer Heteroepitaxy --- p.23 / Chapter 3.2 --- Epitaxial Growth Modes --- p.24 / Chapter 3.2.1 --- Introduction / Chapter 3.2.2 --- Frank-van-der-Merve Mode / Chapter 3.2.3 --- Stranski-Krastanow Mode / Chapter 3.2.4 --- Volmer-Weber Mode / Chapter 3.3 --- Self-assembly of Quantum Dots --- p.30 / Chapter 3.4 --- Current Issues and Problems --- p.30 / Chapter CHAPTER 4: --- EXPERIMENTAL METHODS --- p.34 / Chapter 4.1 --- Equipment --- p.34 / Chapter 4.2 --- Preparation of Sample --- p.34 / Chapter 4.3 --- Growth Rate and Composition Determination --- p.35 / Chapter 4.4 --- Characterization Techniques --- p.40 / Chapter 4.4.1 --- Atomic Force Microscopy (AFM) / Chapter 4.4.2 --- Photoluminescence (PL) / Chapter 4.4.3 --- Other Techniques / Chapter CHAPTER 5: --- RESULTS AND DISCUSSION --- p.44 / Chapter 5.1 --- Introduction --- p.44 / Chapter 5.2 --- Formation Trends of In As QDs --- p.45 / Chapter 5.2.1 --- Experimental Procedures / Chapter 5.2.2 --- Results and Discussion / Chapter 5.2.2.1 --- Effect of Growth Temperature / Chapter 5.2.2.2 --- Effect of Growth Rate / Chapter 5.2.2.3 --- Effect of In As Coverage / Chapter 5.2.2.4 --- Effect of Buffer Layer Material / Chapter 5.2.3 --- Summary / Chapter 5.3 --- Annealing of InAs QDs under Dissimilar Ambient Flux --- p.65 / Chapter 5.3.1 --- Experimental Procedures / Chapter 5.3.2 --- Results and Discussion / Chapter 5.3.3 --- Summary / Chapter CHAPTER 6: --- CONCLUSIONS --- p.75 / Chapter 6.1 --- Summary --- p.75 / Chapter 6.2 --- Future Work --- p.77 / BIBLIOGRAPHY --- p.78 / PUBLICATION LIST --- p.84 / APPENDIX: Abbreviations --- p.85

Yuen Kwun Wan. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves [91]-93). / Text in English; abstracts in English and Chinese. / Yuen Kwun Wan. / Abstract --- p.i / Acknowledgements --- p.ii / Contents --- p.iii / List of Figures --- p.vi / List of Tables --- p.ix / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Formalism of Geometrical Phase --- p.4 / Chapter 2.1 --- Adiabatic cyclic evolution in the parameter space --- p.4 / Chapter 2.2 --- Cyclic evolution of a quantum state on the projective Hilbert space --- p.8 / Chapter 2.3 --- General setting for Berry's phase --- p.11 / Chapter Chapter 3. --- Geometric Phases in Physical Systemms --- p.16 / Chapter 3.1 --- The Aharonov-Bohm Effect --- p.16 / Chapter 3.2 --- An Electron a in Magnetic Field --- p.20 / Chapter 3.2.1 --- The Geometrical Phase in The Adiabatic Limit --- p.22 / Chapter 3.2.2 --- The Geometrical Phases for Other Special Cases --- p.25 / Chapter 3.2.2.1 --- Cyclic Evolution --- p.26 / Chapter 3.2.2.2 --- The Pancharatnam Phase Difference Between ̐ưجψ(t)〉〉〉 and ̐ưجψ(t-pr)〉 --- p.27 / Chapter Chapter 4. --- Review on The Dynamical Cavity Problems --- p.34 / Chapter 4.1 --- Scalar Electrodynamics in a 1-D Cavity with Moving Boundaries --- p.34 / Chapter 4.1.1 --- The Method of Moore's R Function --- p.36 / Chapter 4.1.2 --- Method of Transformation --- p.37 / Chapter 4.2 --- Scalar Electrodynamics in a 1-D Cavity with Oscillating Boundaries --- p.38 / Chapter 4.3 --- Scalar Electrodynamics in a Spherical Cavity with Moving Boundary --- p.39 / Chapter Chapter 5. --- The quantum mechanical phase of a particle in vibrating cavity --- p.41 / Chapter 5.1 --- SU(2) method --- p.48 / Chapter 5.1.1 --- Formalism --- p.48 / Chapter 5.1.2 --- Calculation --- p.51 / Chapter 5.2 --- Rotating Wave Approximation(RWA) --- p.52 / Chapter 5.2.1 --- Formalism --- p.52 / Chapter 5.2.2 --- Behaviors of the system --- p.54 / Chapter 5.2.3 --- Energy --- p.56 / Chapter 5.2.4 --- Geometrical Phases of The System at Resonances --- p.58 / Chapter 5.3 --- Results --- p.63 / Chapter 5.3.1 --- For a Cylindrical Cavity --- p.63 / Chapter 5.4 --- For a Spherical Cavity --- p.70 / Chapter 5.5 --- Conclusion and Discussion --- p.74 / Chapter Chapter 6. --- Summary --- p.76 / Chapter Appendix A. --- Energy Eigenfunctions and Eigenvalues of a Statics Cavity --- p.79 / Chapter A.1 --- For the Case of Cylindrical Cavity --- p.79 / Chapter A.1.1 --- The Energy Eigenfunctions and Corresponding Eigenvalues --- p.81 / Chapter A.2 --- For the Case of Spherical Cavity --- p.81 / Chapter A.2.1 --- The Radial Equation --- p.82 / Chapter A.2.2 --- The Angular Equation --- p.83 / Chapter A.2.3 --- The Energy Eigenfunctions and Corresponding Eigenvalues --- p.84 / Chapter Appendix B. --- The Schrodinger Equation for The Transformed System --- p.85 / Chapter B.1 --- The Schrodinger Equation --- p.85 / Chapter B.2 --- Radial Part of The Schrodinger Equation --- p.86 / Chapter B.2.1 --- For The Case of Cylindrical Cavity --- p.86 / Chapter B.2.2 --- For The Case of Spherical Cavity --- p.87 / Chapter Appendix C. --- Method of Rotating Wave Approximation --- p.88 / Bibliography --- p.91

The field of quantum mechanics has revolutionised physics as a subject. Areas such as information theory, computer science and physical sensing have all been affected by the tremendous successes of various quantum protocols. In this thesis I present my contribution to the development of such non-classical protocols. In classical communication theory a message is always carried by physical particles that interact with a transmitter, after which they travel to a receiver. In this thesis I outline a quantum protocol which allows a receiver to obtain a message without receiving any physical object or particles that have interacted with the transmitter-that is, counterfactually. I build my protocol for counterfactual communication on the principles of interaction-free measurements, ensuring that information always propagates in the opposite direction to the protocol particles. The protocol shows how quantum mechanics breaks the previous premise of communication theory. From the perspective of local observers, it is a beautiful manifestation of the non-locality of interaction-free measurements. Furthermore, it is highly robust against experimental errors and external disturbances. The majority of this part of the thesis is based on my published article 'Quantum counterfactual communication without a weak trace' [Phys. Rev. A 94, 062303 (2016)]. Previous to my work, Salih et al. attempted to design a counterfactual communication protocol [Phys. Rev. Lett. 110, 170502 (2013)]. This protocol has been highly controversial. As counterfactual phenomena impose restrictions on the inter-measurement paths of quantum particles, and the physical reality of such paths lacks description in the Copenhagen interpretation of quantum mechanics, an extension of current quantum theory is required to facilitate a discussion. In this thesis I present an operational and interpretation-independent methodology, enabling the discussion of inter-measurement paths of quantum particles. I start by considering the interferometers of counterfactual protocols, making the basic assumption that any quantum evolution naturally involves uncontrolled weak interactions. I then show how the Fisher information of these weak interactions, available at the output of counterfactual experiments, can be used to discuss the pre-measurement past of the particles. Based on this analysis, the protocol developed by Salih et al. is found to strongly violate counterfactuality. However, my protocol is more flexible in that it allows particles to propagate in the opposite direction to the message. This leads to counterfactuality being satisfied-even in the presence of large experimental errors. These results are observed both analytically and numerically. This part of the thesis is based on my article 'Evaluation of counterfactuality in counterfactual communication protocols' [Phys. Rev. A 96, 062316 (2017)]. The numerical methods are inspired by another of my publications: 'Protocol for fermionic positive-operator-valued measures' [Phys. Rev. A 96, 052305 (2017)]. Finally, as the Fisher information measure is found to be useful in evaluating counterfactual protocols, I extend my work by investigating the quantum Fisher information in experiments with general discrete quantum circuits. I prove that the quantum Fisher information of a two-level interaction in a quantum circuit can be expressed by a simple formula. Under certain phase-relations, the formula provides a straightforward connection between the abstract concept of the inter-measurement wavefunction and the quantum Fisher information at the output. With regard to how the information obtained from a certain volume of space influences our perception of classical objects, I argue that the quantum Fisher information measure is highly useful in describing quantum objects. If this measure is applied to observers with a limited set of the experimental measurement outcomes, a quantum object can appear to follow non-classical discontinuous paths. This supports the remarkable conclusion that our perception of the past of a quantum object is subjectively dependent on the measurement we conduct on it.

Ku, Wai Lim. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 97-100). / Abstracts in English and Chinese. / Ku, Wai Lim. / Chapter 1 --- Review of Entanglement --- p.1 / Chapter 1.1 --- Schmidt Decomposition --- p.1 / Chapter 1.1.1 --- Schmidt Decomposition in Continuous Systems --- p.3 / Chapter 1.2 --- Detecting the Quantum Entanglement of Pure States --- p.5 / Chapter 1.3 --- Quantifying the Quantum Entanglement of Pure States --- p.6 / Chapter 1.3.1 --- Von Neumann entropy --- p.8 / Chapter 1.3.2 --- Purity --- p.8 / Chapter 1.3.3 --- Logarithmic Negativity --- p.9 / Chapter 1.3.4 --- Concurrence --- p.10 / Chapter 2 --- Review of Entanglement in the Relativistic Framework --- p.11 / Chapter 2.1 --- Lorentz Transformation of a Quantum State --- p.11 / Chapter 2.2 --- Unruh effect --- p.14 / Chapter 2.2.1 --- The Rindler Spacetime --- p.14 / Chapter 2.2.2 --- Quantum field theory in Rindler Spacetime --- p.18 / Chapter 2.2.3 --- Lightcone Mode Expansion --- p.21 / Chapter 2.3 --- Entanglement Measured by Uniformly Accelerating Detectors --- p.25 / Chapter 2.3.1 --- Number of States in Rindler Spacetime --- p.26 / Chapter 2.3.2 --- Entanglement in an non-inertial frame --- p.29 / Chapter 2.4 --- Entanglement in an Expanding Universe --- p.32 / Chapter 2.5 --- Summary --- p.36 / Chapter 3 --- Some Topics in Entanglement --- p.37 / Chapter 3.1 --- Introduction --- p.37 / Chapter 3.2 --- Accelerating Schrodinger particles --- p.40 / Chapter 3.3 --- Entanglement of Two-body Wavefuction --- p.43 / Chapter 3.4 --- Accelerating the Relativistic Particles --- p.47 / Chapter 3.4.1 --- Quantization of Fields --- p.47 / Chapter 3.5 --- Accelerating Fermions --- p.51 / Chapter 3.6 --- Accelerating scalar particles --- p.55 / Chapter 3.6.1 --- Spectrum --- p.55 / Chapter 3.6.2 --- Entanglement --- p.55 / Chapter 3.6.3 --- Entanglements if the Number of Produced Pairs is Restricted --- p.57 / Chapter 3.7 --- Discussion of the Accelerating Particles --- p.60 / Chapter 3.8 --- Entanglement in de Sitter space --- p.63 / Chapter 3.8.1 --- Pair Creation in de Sitter space --- p.63 / Chapter 3.8.2 --- Entanglement in the de Sitter space --- p.65 / Chapter 4 --- Review of Geometric Phase --- p.67 / Chapter 4.1 --- Magnetic Aharonov-Bohm Effect --- p.68 / Chapter 4.2 --- Berry Phase --- p.69 / Chapter 4.3 --- Aharonov-Anandan Phase --- p.72 / Chapter 4.4 --- Pancharatnam Phase --- p.73 / Chapter 4.5 --- Geometric Phase in a two-level atom --- p.75 / Chapter 5 --- Relationship Between Entanglement and Geometric Phase --- p.78 / Chapter 5.1 --- Relationship Between Berry's Phase and Concurrence --- p.78 / Chapter 5.2 --- Jaynes-Cummings model --- p.82 / Chapter 5.3 --- Projective Phase in the Jaynes-Cummings model --- p.86 / Chapter A --- The Bogoliubov coefficients in the scalar case --- p.91 / Chapter B --- Reducing the Dirac equations to two Klein-Gordon equations --- p.94 / Bibliography --- p.97