Ho Siu-wai. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaves 103-104). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Classical Information Theory --- p.2 / Chapter 1.1.1 --- Shannon Entropy --- p.3 / Chapter 1.1.2 --- "Shannon Joint Entropy, Conditional Entropy, Mutual Information and Conditional Mutual Information" --- p.5 / Chapter 1.1.3 --- Applications of Shannon Entropy --- p.7 / Chapter 1.2 --- Mathematical background for Quantum Mechanics --- p.8 / Chapter 1.2.1 --- Dirac Notation --- p.8 / Chapter 1.2.2 --- Linear Operators and Matrices --- p.11 / Chapter 1.2.3 --- Spectral Decomposition and Diagonalization --- p.11 / Chapter 1.2.4 --- Functions of Normal Matrices --- p.12 / Chapter 1.2.5 --- Trace --- p.13 / Chapter 1.2.6 --- Kronecker Product --- p.13 / Chapter 1.3 --- Elementary Quantum Mechanics --- p.14 / Chapter 1.3.1 --- State Space --- p.15 / Chapter 1.3.2 --- Evolution --- p.16 / Chapter 1.3.3 --- Quantum Measurements --- p.17 / Chapter 1.3.4 --- Joint Systems --- p.20 / Chapter 1.3.5 --- Quantum Mixtures --- p.22 / Chapter 1.3.6 --- Subsystems --- p.28 / Chapter 1.4 --- von Neumann Entropy --- p.31 / Chapter 1.4.1 --- Definition --- p.32 / Chapter 1.4.2 --- Applications of the von Neumann Entropy --- p.34 / Chapter 1.4.3 --- Conditional Entropy --- p.34 / Chapter 1.5 --- Organization of The Thesis --- p.36 / Chapter Chapter 2 --- Problem Formulations --- p.38 / Chapter 2.1 --- Measurements that Produce Pure States --- p.39 / Chapter 2.2 --- The Shannon Entropy of a Quantum States --- p.41 / Chapter 2.3 --- An Equivalent Density Matrix Obtained by Mixing Orthogonal States --- p.44 / Chapter Chapter 3 --- Pure Post-Measurement States (PPMS) Measurements --- p.46 / Chapter 3.1 --- Introduction --- p.46 / Chapter 3.2 --- Definition of PPMS measurements --- p.46 / Chapter 3.3 --- Properties of PPMS Measurement --- p.52 / Chapter 3.4 --- An Alternative Definition of von Neumann entropy in terms of PPMS Measurements --- p.73 / Chapter Chapter 4 --- Mental Measurement of a Quantum State --- p.75 / Chapter 4.1 --- Introduction --- p.75 / Chapter 4.2 --- An Alternative Definition of a Projective Measurement --- p.76 / Chapter 4.3 --- Characteristics of a Projective PPMS Measurement --- p.81 / Chapter 4.4 --- The Choice of the Mental Measurement --- p.84 / Chapter 4.5 --- An Alternative Definition of von Neumann Entropy by Means of a Mental Measurement --- p.86 / Chapter 4.6 --- Construction of the Mental Measurement --- p.86 / Chapter Chapter 5 --- Completeness of Density Matrix Postulate --- p.92 / Chapter 5.1 --- Introduction --- p.92 / Chapter 5.2 --- Complete Specification of Quantum Ensemble by Density Matrix --- p.93 / Chapter 5.3 --- An Alternative Definition of von Neumann Entropy by Shannon Entropy --- p.98 / Chapter Chapter 6 --- Conclusion and Future Works --- p.99 / Chapter 6.1 --- Conclusion --- p.99 / Chapter 6.2 --- Future Work --- p.101 / Reference --- p.103
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_324186 |
| Date | January 2003 |
| Contributors | Ho, Siu-wai., Chinese University of Hong Kong Graduate School. Division of Information Engineering. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, ix, 106 leaves : ill. ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
Page generated in 0.0023 seconds