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In quantum mechanics, and especially quantum information theory, the linear entropy or impurity of a state is a scalar defined as : where ''ρ'' is the density matrix of the state. The linear entropy can range between zero, corresponding to a completely pure state, and (1 − 1/''d''), corresponding to a completely mixed state. (Here, ''d'' is the dimension of the density matrix.) The linear entropy is trivially related to the purity of a state by : ==Motivation== The linear entropy is a lower approximation to the (quantum) von Neumann entropy ''S'', which is defined as : The linear entropy then is obtained by expanding ln ''ρ'' = ln (1−(1−''ρ'')), around a pure state, ''ρ''2=''ρ''; that is, expanding in terms of the non-negative matrix 1−''ρ'' in the formal Mercator series for the logarithm, : and retaining just the leading term. The linear entropy and von Neumann entropy are similar measures of the degree of mixing of a state, although the linear entropy is easier to calculate, as it does not require diagonalization of the density matrix. 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「Linear entropy」の詳細全文を読む スポンサード リンク
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