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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 , are finite-dimensional vector spaces over a field, with dimensions and , respectively. For any space let denote the space of linear operators on . The partial trace over , , is a mapping : It is defined as follows: let : and : be bases for ''V'' and ''W'' respectively; then ''T'' has a matrix representation : relative to the basis : of :. Now for indices ''k'', ''i'' in the range 1, ..., ''m'', consider the sum : 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
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