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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 Typical subspace ： ウィキペディア英語版 Typical subspace In quantum information theory, the idea of a typical subspace plays an important role in the proofs of many coding theorems (the most prominent example being Schumacher compression). Its role is analogous to that of the typical set in classical information theory. == Unconditional Quantum Typicality == Consider a density operator $\backslash rho$ with the following spectral decomposition: :$$ \rho=\sum_p_\left( x\right) \left\vert x\right\rangle \left\langle x\right\vert . The weakly typical subspace is defined as the span of all vectors such that the sample entropy $\backslash overline\backslash left(\; x^\backslash right)$ of their classical label is close to the true entropy $H\backslash left(\; X\backslash right)$ of the distribution $p\_\backslash left(\; x\backslash right)$: :$$ T_^\left\\left( x^\right) -H\left( X\right) \right\vert \leq\delta\right\} , where :$$ \overline\left( x^\right) \equiv-\frac\log\left( p_\left( x^\right) \right) , :$H\backslash left(\; X\backslash right)\; \backslash equiv-\backslash sum\_p\_\backslash left(\; x\backslash right)\; \backslash log\; p\_\backslash left($ x\right) . The projector $\backslash Pi\_^$ onto the typical subspace of $\backslash rho$ is defined as :$$ \Pi_^\equiv\sum_^\left\vert x^\right\rangle \left\langle x^\right\vert , where we have "overloaded" the symbol $T\_^^:\backslash left\backslash vert\; \backslash overline\backslash left($ x^\right) -H\left( X\right) \right\vert \leq\delta\right\} . The three important properties of the typical projector are as follows: :$$ \text\left\\rho^\right\} \geq1-\epsilon, :$\backslash text\backslash left\backslash \backslash right\backslash \}\; \backslash leq2^,$ :$2^\backslash Pi\_^$ \leq\Pi_^\rho^\Pi_^\leq2^\Pi_^, where the first property holds for arbitrary $\backslash epsilon,\backslash delta>0$ and sufficiently large $n$. 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「Typical subspace」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.