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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 Partial trace ： ウィキペディア英語版 Partial trace In linear algebra and functional analysis, the partial trace is a generalization of the trace. Whereas the trace is a scalar valued function on operators, the partial trace is an operator-valued function. The partial trace has applications in quantum information and decoherence which is relevant for quantum measurement and thereby to the decoherent approaches to interpretations of quantum mechanics, including consistent histories and the relative state interpretation. == Details == Suppose $V$, $W$ are finite-dimensional vector spaces over a field, with dimensions $m$ and $n$, respectively. For any space $A$ let $L(A)$ denote the space of linear operators on $A$. The partial trace over $W$, $\backslash operatorname\_W:\; \backslash operatorname(V\; \backslash otimes\; W)\; \backslash to\; \backslash operatorname(V)$, is a mapping :$T\; \backslash in\; \backslash operatorname(V\; \backslash otimes\; W)\; \backslash mapsto\; \backslash operatorname\_W\; (T)\; \backslash in\; \backslash operatorname(V)$ It is defined as follows: let :$e\_1,\; \backslash ldots,\; e\_m$ and :$f\_1,\; \backslash ldots,\; f\_n$ be bases for ''V'' and ''W'' respectively; then ''T'' has a matrix representation :$\backslash \; \backslash quad\; 1\; \backslash leq\; k,\; i\; \backslash leq\; m,\; \backslash quad\; 1\; \backslash leq\; \backslash ell,j\; \backslash leq\; n$ relative to the basis :$e\_k\; \backslash otimes\; f\_\backslash ell$ of :$V\; \backslash otimes\; W$. Now for indices ''k'', ''i'' in the range 1, ..., ''m'', consider the sum :$b\_\; =\; \backslash sum\_^n\; a\_.$ This gives a matrix ''b''''k'', ''i''. The associated linear operator on ''V'' is independent of the choice of bases and is by definition the partial trace. Among physicists, this is often called "tracing out" or "tracing over" ''W'' to leave only an operator on ''V'' in the context where ''W'' and ''V'' are Hilbert spaces associated with quantum systems (see below). 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「Partial trace」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.