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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 quantum mutual information ： ウィキペディア英語版 quantum mutual information In quantum information theory, quantum mutual information, or von Neumann mutual information, after John von Neumann, is a measure of correlation between subsystems of quantum state. It is the quantum mechanical analog of Shannon mutual information. == Motivation == For simplicity, it will be assumed that all objects in the article are finite-dimensional. The definition of quantum mutual entropy is motivated by the classical case. For a probability distribution of two variables ''p''(''x'', ''y''), the two marginal distributions are :$p(x)\; =\; \backslash sum\_\; p(x,y)\backslash ;\; ,\; \backslash ;\; p(y)\; =\; \backslash sum\_\; p(x,y).$ The classical mutual information ''I''(''X'', ''Y'') is defined by :$\backslash ;I(X,Y)\; =\; S(p(x))\; +\; S(p(y))\; -\; S(p(x,y))$ where ''S''(''q'') denotes the Shannon entropy of the probability distribution ''q''. One can calculate directly :$\backslash ;\; S(p(x))\; +\; S(p(y))$ :$\backslash ;\; =\; -(\backslash sum\_x\; p\_x\; \backslash log\; p(x)\; +\; \backslash sum\_y\; p\_y\; \backslash log\; p(y))$ :$$ \; = -(\sum_x \; ( \sum_ p(x,y') \log \sum_ p(x,y') ) + \sum_y ( \sum_ p(x',y) \log \sum_ p(x',y))) :$\backslash ;\; =\; -(\backslash sum\_\; p(x,y)\; (\backslash log\; \backslash sum\_\; p(x,y\text{'})\; +\; \backslash log\; \backslash sum\_\; p(x\text{'},y)))$ :$\backslash ;\; =\; -\backslash sum\_\; p(x,y)\; \backslash log\; p(x)\; p(y)\; .$ So the mutual information is :$I(X,Y)\; =\; \backslash sum\_\; p(x,y)\; \backslash log\; \backslash frac.$ But this is precisely the relative entropy between ''p''(''x'', ''y'') and ''p''(''x'')''p''(''y''). In other words, if we assume the two variables ''x'' and ''y'' to be uncorrelated, mutual information is the ''discrepancy in uncertainty'' resulting from this (possibly erroneous) assumption. It follows from the property of relative entropy that ''I''(''X'',''Y'') ≥ 0 and equality holds if and only if ''p''(''x'', ''y'') = ''p''(''x'')''p''(''y''). 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「quantum mutual information」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.