On the relation between the Shannon entropy and the von Neumann entropy.

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.1Chapter 1.1 --- Classical Information Theory --- p.2Chapter 1.1.1 --- Shannon Entropy --- p.3Chapter 1.1.2 --- "Shannon Joint Entropy, Conditional Entropy, Mutual Information and Conditional Mutual Information" --- p.5Chapter 1.1.3 --- Applications of Shannon Entropy --- p.7Chapter 1.2 --- Mathematical background for Quantum Mechanics --- p.8Chapter 1.2.1 --- Dirac Notation --- p.8Chapter 1.2.2 --- Linear Operators and Matrices --- p.11Chapter 1.2.3 --- Spectral Decomposition and Diagonalization --- p.11Chapter 1.2.4 --- Functions of Normal Matrices --- p.12Chapter 1.2.5 --- Trace --- p.13Chapter 1.2.6 --- Kronecker Product --- p.13Chapter 1.3 --- Elementary Quantum Mechanics --- p.14Chapter 1.3.1 --- State Space --- p.15Chapter 1.3.2 --- Evolution --- p.16Chapter 1.3.3 --- Quantum Measurements --- p.17Chapter 1.3.4 --- Joint Systems --- p.20Chapter 1.3.5 --- Quantum Mixtures --- p.22Chapter 1.3.6 --- Subsystems --- p.28Chapter 1.4 --- von Neumann Entropy --- p.31Chapter 1.4.1 --- Definition --- p.32Chapter 1.4.2 --- Applications of the von Neumann Entropy --- p.34Chapter 1.4.3 --- Conditional Entropy --- p.34Chapter 1.5 --- Organization of The Thesis --- p.36Chapter Chapter 2 --- Problem Formulations --- p.38Chapter 2.1 --- Measurements that Produce Pure States --- p.39Chapter 2.2 --- The Shannon Entropy of a Quantum States --- p.41Chapter 2.3 --- An Equivalent Density Matrix Obtained by Mixing Orthogonal States --- p.44Chapter Chapter 3 --- Pure Post-Measurement States (PPMS) Measurements --- p.46Chapter 3.1 --- Introduction --- p.46Chapter 3.2 --- Definition of PPMS measurements --- p.46Chapter 3.3 --- Properties of PPMS Measurement --- p.52Chapter 3.4 --- An Alternative Definition of von Neumann entropy in terms of PPMS Measurements --- p.73Chapter Chapter 4 --- Mental Measurement of a Quantum State --- p.75Chapter 4.1 --- Introduction --- p.75Chapter 4.2 --- An Alternative Definition of a Projective Measurement --- p.76Chapter 4.3 --- Characteristics of a Projective PPMS Measurement --- p.81Chapter 4.4 --- The Choice of the Mental Measurement --- p.84Chapter 4.5 --- An Alternative Definition of von Neumann Entropy by Means of a Mental Measurement --- p.86Chapter 4.6 --- Construction of the Mental Measurement --- p.86Chapter Chapter 5 --- Completeness of Density Matrix Postulate --- p.92Chapter 5.1 --- Introduction --- p.92Chapter 5.2 --- Complete Specification of Quantum Ensemble by Density Matrix --- p.93Chapter 5.3 --- An Alternative Definition of von Neumann Entropy by Shannon Entropy --- p.98Chapter Chapter 6 --- Conclusion and Future Works --- p.99Chapter 6.1 --- Conclusion --- p.99Chapter 6.2 --- Future Work --- p.101Reference --- p.10