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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 Generalized relative entropy ： ウィキペディア英語版 Generalized relative entropy Generalized relative entropy ($\backslash epsilon$-relative entropy) is a measure of dissimilarity between two quantum states. It is a "one-shot" analogue of quantum relative entropy and shares many properties of the latter quantity. In the study of quantum information theory, we typically assume that information processing tasks are repeated multiple times, independently. The corresponding information-theoretic notions are therefore defined in the asymptotic limit. The quintessential entropy measure, von Neumann entropy, is one such notion. In contrast, the study of one-shot quantum information theory is concerned with information processing when a task is conducted only once. New entropic measures emerge in this scenario, as traditional notions cease to give a precise characterization of resource requirements. $\backslash epsilon$-relative entropy is one such particularly interesting measure. In the asymptotic scenario, relative entropy acts as a parent quantity for other measures besides being an important measure itself. Similarly, $\backslash epsilon$-relative entropy functions as a parent quantity for other measures in the one-shot scenario. == Definition == To motivate the definition of the $\backslash epsilon$-relative entropy $D^(\backslash rho||\backslash sigma)$, consider the information processing task of hypothesis testing. In hypothesis testing, we wish to devise a strategy to distinguish between two density operators $\backslash rho$ and $\backslash sigma$. A strategy is a POVM with elements $Q$ and $I\; -\; Q$. The probability that the strategy produces a correct guess on input $\backslash rho$ is given by $\backslash operatorname(\backslash rho\; Q)$ and the probability that it produces a wrong guess is given by $\backslash operatorname(\backslash sigma\; Q)$. $\backslash epsilon$-relative entropy captures the minimum probability of error when the state is $\backslash sigma$, given that the success probability for $\backslash rho$ is at least $\backslash epsilon$. For $\backslash epsilon\; \backslash in\; (0,1)$, the $\backslash epsilon$-relative entropy between two quantum states$\backslash rho$ and $\backslash sigma$ is defined as :::$D^(\backslash rho||\backslash sigma)\; =\; -\; \backslash log\; \backslash frac\; \backslash min\; \backslash \; ~.$ From the definition, it is clear that $D^(\backslash rho||\backslash sigma)\backslash geq\; 0$. This inequality is saturated if and only if $\backslash rho\; =\; \backslash sigma$, as shown below. 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「Generalized relative 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.