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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Wehrl entropy ： ウィキペディア英語版 Wehrl entropy In quantum information theory, the Wehrl entropy, named after A. Wehrl, is a type of quasi-entropy defined for the Husimi Q representation 〔Kôdi Husimi (1940). "Some Formal Properties of the Density Matrix", ''Proc. Phys. Math. Soc. Jpn.'' 22: 264–314 .〕 of the phase-space quasiprobability distribution. It is defined as :$S\_Q\; =\; -\backslash int\; Q(x,p)\; \backslash log\; Q(x,p)\; \backslash ,\; dx\; \backslash ,\; dp\; ~.$ Such a definition of entropy relies on the fact that the Husimi Q representation remains non-negative definite, unlike other representations of quantum quasiprobability distributions in phase space. However, it is not the fully quantum von Neumann entropy in the Husimi representation in phase space, : all the requisite star-products ★ in that entropy have been dropped here. In the Husimi representation, the star products read :$\backslash star\; \backslash equiv\; \backslash exp\backslash left(\; \backslash frac$ (}_x -i }_p) (}_x + i}_p ) \right)~, and are isomorphic〔C. Zachos, D. Fairlie, and T. Curtright, “Quantum Mechanics in Phase Space” (''World Scientific'', Singapore, 2005) ISBN 978-981-238-384-6 .〕 to the Moyal products of the Wigner–Weyl representation. The Wehrl entropy, then, may be thought of as a type of heuristic semiclassical approximation to the full quantum von Neumann entropy, since it retains some dependence (through ''Q'') but ''not all of it''. Like all entropies, it reflects some measure of non-localization,〔 〕 as the Gauss transform involved in generating and the sacrifice of the star operators have effectively discarded information. In general, for the same state, the Wehrl entropy exceeds the von Neumann entropy (which vanishes for pure states). ==References== 〔 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Wehrl entropy」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.