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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 Werner state ： ウィキペディア英語版 Werner state A Werner state〔 〕 is a -dimensional bipartite quantum state density matrix that is invariant under all unitary operators of the form $U\; \backslash otimes\; U$. That is, it is a quantum state ''ρ'' that satisfies :$\backslash rho\; =\; (U\; \backslash otimes\; U)\; \backslash rho\; (U^\backslash dagger\; \backslash otimes\; U^\backslash dagger)$ for all unitary operators ''U'' acting on ''d''-dimensional Hilbert space. Every Werner state is a mixture of projectors onto the symmetric and antisymmetric subspaces, with the relative weight ''p''sym being the only parameter that defines the state. :$\backslash rho\; =\; p\_\backslash text\; \backslash frac\; P\_\backslash text\; +\; (1-p\_\backslash text)\; \backslash frac\; P\_\backslash text,$ where :$P\_\backslash text\; =\; \backslash frac(1+P),$ $P\_\backslash text\; =\; \backslash frac(1-P),$ are the projectors and :$P\; =\; \backslash sum\_\; |i\backslash rangle\; \backslash langle\; j|\; \backslash otimes\; |j\backslash rangle\; \backslash langle\; i|$ is the permutation operator that exchanges the two subsystems. Werner states are separable for ''p''sym ≥ and entangled for ''p''sym < . All entangled Werner states violate the PPT separability criterion, but for ''d'' ≥ 3 no Werner states violate the weaker reduction criterion. Werner states can be parametrized in different ways. One way of writing them is :$\backslash rho\; =\; \backslash frac(1\; -\; \backslash alpha\; P),$ where the new parameter ''α'' varies between −1 and 1 and relates to ''p''sym as :$\backslash alpha\; =\; ((1-2p\_\backslash text)d+1)/(1-2p\_\backslash text+d)\; .$ == Multipartite Werner states == Werner states can be generalized to the multipartite case.〔Eggeling ''et al.'' (2008)〕 An ''N''-party Werner state is a state that is invariant under $U\; \backslash otimes\; U\; \backslash otimes\; ...\; \backslash otimes\; U$ for any unitary ''U'' on a single subsystem. The Werner state is no longer described by a single parameter, but by ''N''! − 1 parameters, and is a linear combination of the ''N''! different permutations on ''N'' systems. 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「Werner state」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.