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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 Peres–Horodecki criterion ： ウィキペディア英語版 Peres–Horodecki criterion The Peres–Horodecki criterion is a necessary condition, for the joint density matrix $\backslash rho$ of two quantum mechanical systems $A$ and $B$, to be separable. It is also called the PPT criterion, for ''positive partial transpose''. In the 2x2 and 2x3 dimensional cases the condition is also sufficient. It is used to decide the separability of mixed states, where the Schmidt decomposition does not apply. In higher dimensions, the test is inconclusive, and one should supplement it with more advanced tests, such as those based on entanglement witnesses. ==Definition== If we have a general state $\backslash rho$ which acts on $\backslash mathcal\_A\; \backslash otimes\; \backslash mathcal\_B$ :$\backslash rho\; =\; \backslash sum\_\; p^\_\; |i\backslash rangle\; \backslash langle\; j\; |\; \backslash otimes\; |k\backslash rangle\; \backslash langle\; l|$ Its partial transpose (with respect to the B party) is defined as :$\backslash rho^\; :=\; I\; \backslash otimes\; T\; (\backslash rho)\; =\; \backslash sum\_\; p^\; \_\; |i\backslash rangle\; \backslash langle\; j\; |\; \backslash otimes\; (|k\backslash rangle\; \backslash langle\; l|)^T\; =\; \backslash sum\_\; p^\; \_\; |i\backslash rangle\; \backslash langle\; j\; |\; \backslash otimes\; |l\backslash rangle\; \backslash langle\; k|$ Note that the ''partial'' in the name implies that only part of the state is transposed. More precisely, $I\; \backslash otimes\; T\; (\backslash rho)$ is the identity map applied to the A party and the transposition map applied to the B party. This definition can be seen more clearly if we write the state as a block matrix: : Where $n\; =\; \backslash dim\; \backslash mathcal\_A$, and each block is a square matrix of dimension $m\; =\; \backslash dim\; \backslash mathcal\_B$. Then the partial transpose is : The criterion states that if $\backslash rho\backslash ;\backslash !$ is separable, $\backslash rho^$ has non-negative eigenvalues. In other words, if $\backslash rho^$ has a negative eigenvalue, $\backslash rho\backslash ;\backslash !$ is guaranteed to be entangled. If the eigenvalues are non-negative, and the dimension is larger than 6, the test is inconclusive. The result is independent of the party that was transposed, because $\backslash rho^\; =\; (\backslash rho^)^T$. 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「Peres–Horodecki criterion」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.