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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 Separable state ： ウィキペディア英語版 Separable state In quantum mechanics, separable quantum states are states without quantum entanglement. == Separable pure states == For simplicity, the following assumes all relevant state spaces are finite-dimensional. First, consider separability for pure states. Let $H\_1$ and $H\_2$ be quantum mechanical state spaces, that is, finite-dimensional Hilbert spaces with basis states $\backslash \_^n$ and $\backslash \_^m$, respectively. By a postulate of quantum mechanics, the state space of the composite system is given by the tensor product :$H\_1\; \backslash otimes\; H\_2$ with base states $\backslash \backslash rangle\backslash \}$, or in more compact notation $\backslash$. From the very definition of the tensor product, any vector of norm 1, i.e. a pure state of the composite system, can be written as : $$ |\psi\rangle = \sum_ c_ (| a_i \rangle \otimes | b_j \rangle) =\sum_ c_ | a_i b_j \rangle If a pure state $|\backslash psi\backslash rangle\; \backslash in\; H\_1\; \backslash otimes\; H\_2$ can be written in the form $|\backslash psi\backslash rangle\; =\; |\backslash psi\_1\backslash rangle\; \backslash otimes\; |\backslash psi\_2\backslash rangle$ where $|\backslash psi\; \_i\; \backslash rangle$ is a pure state of the i-th subsystem, it is said to be ''separable''. Otherwise it is called ''entangled''. When a system is in an entangled pure state, it is not possible to assign states to its subsystems. This will be true, in the appropriate sense, for the mixed state case as well. Formally, the embedding of a product of states into the product space is given by the Segre embedding. That is, a quantum-mechanical pure state is separable if and only if it is in the image of the Segre embedding. The above discussion can be extended to the case of when the state space is infinite-dimensional with virtually nothing changed. 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「Separable 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.