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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 Trace distance ： ウィキペディア英語版 Trace distance In quantum mechanics, and especially quantum information and the study of open quantum systems, the trace distance ''T'' is a metric on the space of density matrices and gives a measure of the distinguishability between two states. It is the quantum generalization of the Kolmogorov distance for classical probability distributions. == Definition == The trace distance is just half of the trace norm of the difference of the matrices: :$T(\backslash rho,\backslash sigma)\; :=\; \backslash frac||\backslash rho\; -\; \backslash sigma||\_\; =\; \backslash frac\; \backslash mathrm\; \backslash left(\backslash sqrt\; \backslash right)\; .$ (The trace norm is the Schatten norm for ''p''=1.) The purpose of the factor of two is to restrict the trace distance between two normalized density matrices to the range () and to simplify formulas in which the trace distance appears. Since density matrices are Hermitian, :$T(\backslash rho,\backslash sigma)\; =\; \backslash frac\; \backslash mathrm\; \backslash left(\backslash sqrt\; \backslash right)\; =\; \backslash frac\; \backslash sum\_i\; |\; \backslash lambda\_i\; |\; ,$ where the $\backslash lambda\_i$ are eigenvalues of the Hermitian, but not necessarily positive, matrix $(\backslash rho-\backslash sigma)$. 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「Trace distance」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.