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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 Geometric measure of entanglement ： ウィキペディア英語版 Geometric measure of entanglement The geometric measure of entanglement is a means to quantify the entanglement in a multi-partite system. For a system consisting of $N$ subsystems, the full Hilbert space $\backslash mathcal$ is a tensor product of those of the subsystems, i.e., $\backslash mathcal\; =\; \backslash mathcal\_1\; \backslash otimes\; \backslash mathcal\_2\; \backslash ldots\; \backslash otimes\; \backslash mathcal\_N$. But for a generic state $\backslash psi\; \backslash in\; \backslash mathcal$, it is impossible to write it as a tensor product state. That is, it is impossible to write it in the form of $\backslash psi\; =\; \backslash psi\_1\; \backslash otimes\; \backslash psi\_2$ \ldots \otimes \psi_N , with $\backslash psi\_i\; \backslash in\; \backslash mathcal\_i$. This implies the existence of entanglement between the subsystems. The geometric measure of entanglement in $\backslash psi$ (with $\backslash langle\; \backslash psi|\backslash psi\; \backslash rangle\; =\; 1$) is then quantified by the minimum of :$\backslash |\; \backslash psi\; -\; \backslash phi\; \backslash |$ with respect to all the separable states :$\backslash phi\; =\; \backslash prod\_^N\; \backslash otimes\; \backslash phi\_i\; ,$ with $\backslash langle\; \backslash phi\_i|\backslash phi\_i\; \backslash rangle\; =\; 1$. This approach works for distinguishable particles or the spin systems. For identical or indistinguishable fermions or bosons, the full Hilbert space is not the tensor product of those of each individual particle. Therefore, a simple modification is necessary. For example, for identical fermions, since the full wave function $\backslash psi$ is now completely anti-symmetric, so is required for $\backslash phi$. This means, the $\backslash phi$ taken to approximate $\backslash psi$ should be a Slater determinant wave function. ==References== 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「Geometric measure of entanglement」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.