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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 fidelity ： ウィキペディア英語版 Fidelity of quantum states In quantum information theory, fidelity is a measure of the "closeness" of two quantum states. It is not a metric on the space of density matrices, but it can be used to define the Bures metric on this space. == Motivation == Given two random variables ''X'', ''Y'' with values (1...n) and probabilities ''p'' = (''p''1...''pn'') and ''q'' = (''q''1...''qn''). The fidelity of ''X'' and ''Y'' is defined to be the quantity :$F(X,Y)\; =\; \backslash sum\; \_i\; \backslash sqrt$. The fidelity deals with the marginal distribution of the random variables. It says nothing about the joint distribution of those variables. In other words, the fidelity ''F(X,Y)'' is the inner product of $(\backslash sqrt,\; \backslash cdots\; ,\backslash sqrt)$ and $(\backslash sqrt,\; \backslash cdots\; ,\backslash sqrt)$ viewed as vectors in Euclidean space. Notice that ''F(X,Y)'' = 1 if and only if ''p'' = ''q''. In general, $0\; \backslash leq\; F(X,Y)\; \backslash leq\; 1$. This measure is known as the Bhattacharyya coefficient. Given a classical measure of the distinguishability of two probability distributions, one can motivate a measure of distinguishability of two quantum states as follows. If an experimenter is attempting to determine whether a quantum state is either of two possibilities $\backslash rho$ or $\backslash sigma$, the most general possible measurement he can make on the state is a POVM, which is described by a set of Hermitian positive semidefinite operators $\backslash$. If the state given to the experimenter is $\backslash rho$, he will witness outcome $i$ with probability $p\_i\; =\; \backslash mathrm(\backslash rho\; F\_i)$, and likewise with probability $q\_i\; =\; \backslash mathrm(\backslash sigma\; F\_i)$ for $\backslash sigma$. His ability to distinguish between the quantum states $\backslash rho$ and $\backslash sigma$ is then equivalent to his ability to distinguish between the classical probability distributions $p$ and $q$. Naturally, the experimenter will choose the best POVM he can find, so this motivates defining the quantum fidelity as the Bhattacharyya coefficient when extremized over all possible POVMs $\backslash$: :$F(\backslash rho,\backslash sigma)\; =\; \backslash min\_\}\; \backslash sum\; \_i\; \backslash sqrt(\backslash sigma\; F\_i)\}$. It was shown by Fuchs and Caves that this manifestly symmetric definition is equivalent to the simple asymmetric formula given in the next section.〔C. A. Fuchs, C. M. Caves: ("Ensemble-Dependent Bounds for Accessible Information in Quantum Mechanics" ), ''Physical Review Letters'' 73, 3047(1994)〕 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「Fidelity of quantum states」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.