Lo Ying Hang. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. / Includes bibliographical references (leaves 80-81). / Abstracts in English and Chinese. / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Background --- p.4 / Chapter Chapter 3 --- Commutative Partition Pair Analysis --- p.9 / Chapter Chapter 4 --- Entropy Inequalities for Partition Pair --- p.19 / Chapter Chapter 5 --- Entropy Characterization of Commutative Partition Pair --- p.32 / Chapter Chapter 6 --- Ordered Commutative Partitions --- p.43 / Chapter Chapter 7 --- Running Intersection Property for Partitions --- p.45 / Chapter Chapter 8 --- Entropy Characterization of Ordered Commutative Partitions --- p.53 / Chapter Chapter 9 --- Significance and Application --- p.72 / Chapter Chapter 10 --- Future Plan --- p.78 / Chapter Chapter 11 --- Conclusion --- p.79 / Bibliography --- p.80

令N = {1, ..., n}. 一組n個隨機變量{Xi : i ∈ N} 的熵函數h是一個2n維的向量，該向量的每個分量h(A) = H(XA);A ⊂ N, 即該組隨機變量的子集的(聯合)熵且空集的熵按傳統看做為0。所有n個隨機變量的熵函數組成的區 域稱為n階熵函數區域，記作Γ* n。熵函數區域Γ* n及其閉包Γ* n的表徵是信息論中著名的開放問題。 / 在本文中，我們研究劃分對稱熵函數。令p = {N₁... ,Nt}為N的 一個t-劃分 。一個熵函數h稱為p-對稱的，若h滿足:對於N的所有子集A，B，對於p的每一 個分塊，只要A和該分塊的交集的基數與B和該分塊交集的基數相等，那麼h(A) = h(B)。所有p-對稱熵函數的集合稱作p-對稱熵函數區域。我們證明p-對稱熵函數區域的 閉包可以由香農型信息不等式完全表徵當且僅當p為1-劃分或者有一個分塊為單元 素集合的2-劃分。 / 劃分對稱熵函數的表徵能應用於那些結構中含有對稱的信息論問題及其相關問題。 / Let N = {1, ..., n}. The entropy function h of a set of n discrete randomvariables {Xi : i ∈ N} is a 2n-dimensional vector whose entries are h(A)H(XA),ACN, the (joint) entropies of the subsets of the set of n randomvariables with H(X) = 0 by convention. The set of all entropy functions for n discrete random variables, denoted by Γ* n , is called the entropy function region for n. Characterization of Γ* n and its closure Γ* n are well-known open problems in information theory. They are important not only because they play key roles in information theory problems but also they are related to other subjects in mathematics and physics. / In this thesis, we consider partition-symmetrical entropy functions. Let p ={N₁... ,Nt} be a t-partition of N. An entropy function h is called p-symmetricalif for all A,B ⊂ N, h(A) = h(B) whenever / The characterization of the partition-symmetrical entropy functions can beuseful for solving some information theory and related problems where symmetryexists in the structure of the problems. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Chen, Qi. / Thesis (Ph.D.) Chinese University of Hong Kong, 2014. / Includes bibliographical references (leaves 70-73). / Abstracts also in Chinese.

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

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (p. 155-161).

published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

Thesis (Ph. D.)--University of New South Wales, 1997. / Also available online.

Thesis (Ph. D.)--Oregon State University, 2009. / Printout. Includes bibliographical references (leaves 88-89). Also available on the World Wide Web.

Thesis (M. Phil.)--University of Hong Kong, 1996. / Includes bibliographical references (leaf 141-146).

Thesis (Ph. D.)--University of New South Wales, 1997. / Completed at: University of New South Wales, School of Mathematics. Title from electronic deposit form.

Thesis (Ph. D.)--University of Chicago, Dept. of Statistics, June 1999. / Includes bibliographical references. Also available on the Internet.