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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 Superoperator ： ウィキペディア英語版 Superoperator In physics, a superoperator is a linear operator acting on a vector space of linear operators.〔John Preskill, Lecture notes for Quantum Computation course at Caltech, (Ch. 3 ), ()〕 Sometimes the term refers more specially to a completely positive map which does not increase or preserves the trace of its argument. This specialized meaning is used extensively in the field of quantum computing, especially quantum programming, as they characterise mappings between density matrices. The use of the super- prefix here is in no way related to its other use in mathematical physics. That is to say superoperators have no connection to supersymmetry and superalgebra which are extensions of the usual mathematical concepts defined by extending the ring of numbers to include Grassmann numbers. Since superoperators are themselves operators the use of the super- prefix is used to distinguish them from the operators upon which they act. ==Example von Neumann Equation== In quantum mechanics the Schrödinger Equation, $i\; \backslash hbar\; \backslash frac\backslash Psi\; =\; \backslash hat\; H\; \backslash Psi$ expresses the time evolution of the state vector $\backslash psi$ by the action of the Hamiltonian $\backslash hat$ which is an operator mapping state vectors to state vectors. In the more general formulation of John von Neumann, statistical states and ensembles are expressed by density operators rather than state vectors. In this context the time evolution of the density operator is expressed via the von Neumann equation in which density operator is acted upon by a superoperator $\backslash mathcal$ mapping operators to operators. It is defined by taking the commutator with respect to the Hamiltonian operator: $i\; \backslash hbar\; \backslash frac\backslash rho\; =\; \backslash mathcal()$ where $\backslash mathcal()\; =\; ()\; \backslash equiv\; \backslash hat\backslash rho\; -\; \backslash rho\backslash hat$ As commutator brackets are used extensively in QM this explicit superoperator presentation of the Hamiltonian's action is typically omitted. 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「Superoperator」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.