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熵与信息的多少性质及应用.pdf 93页

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熵与信息的多少性质及应用
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 ()  Zhang ()  Shannon von Neumann ( Tsallis ) ◦ 45 . ℄  Barnum Piani I  II Abstract The concept of entropy has its origin in thermodynamics, and is fundamental in quantifying randomness and uncertainties of states. Entropy and its various derivatives such as relative entropy and mutual information play an important role in both classical and quantum information theory. In this paper, some properties and applications of generalized entropy, quantum relative entropy and quantum information are studied. The stability of entropy is a basic and important issue. In Chapter 2, the stabilities of both classical and quantum generalized entropy are discussed for finite systems. By use of a probabilistic coupling technique introduced by Zhang, several sharp inequalities concerning the uniform continuity of some generalized entropies have been obtained, which generalize some existing results such as the stabilities of Shannon entropy, von Neumann entropy

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