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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 SIC-POVM ： ウィキペディア英語版 SIC-POVM A symmetric, informationally complete, positive operator valued measure (SIC-POVM) is a special case of a generalized measurement on a Hilbert space, used in the field of quantum mechanics. A measurement of the prescribed form satisfies certain defining qualities that makes it an interesting candidate for a "standard quantum measurement," utilized in the study of foundational quantum mechanics. Furthermore, it has been shown that applications exist in quantum state tomography〔C. M. Caves, C. A. Fuchs, and R. Schack, “Unknown Quantum States: The Quantum de Finetti Representation,” J. Math. Phys. 43, 4537–4559 (2002).〕 and quantum cryptography.〔C. A. Fuchs and M. Sasaki, “Squeezing Quantum Information through a Classical Channel: Measuring the ‘Quantumness’ of a Set of Quantum States,” Quant. Info. Comp. 3, 377–404 (2003).〕 ==Definition== Due to the use of SIC-POVMs primarily in quantum mechanics, Dirac notation will be used to represent elements associated with the Hilbert space. In general, a POVM over a $d$-dimensional Hilbert space $\backslash mathcal$ is defined as a set $M$ of positive semidefinite operators $\backslash$ on the Hilbert space that sum to the identity: :$\backslash sum\_^M\; F\_i\; =\; I.$ A SIC-POVM is more restrictive in that the operators must be subnormalized projectors related to one another such that they have the properties of symmetry and informational completeness. In this context informational completeness means that the probabilities of observing the various outcomes entirely determines any quantum state being measured by the scheme. This requires $d^2$ linearly independent operators. Symmetry means that the inner product of all pairs of subnormalized projectors $F\_i,F\_j$ is a constant: :$\backslash mathrm\backslash left(\; F\_i\; F\_j\; \backslash right)\; =\; \backslash frac\; =\; \backslash frac\; =\; \backslash frac\; \backslash quad\; i\; \backslash ne\; j.$ The combination of symmetry and informational completeness means $M$ is composed entirely of operators of the form :$F\_i=\backslash frac\; \backslash Pi\_i,$ where $\backslash Pi\_i$ is a rank-one projector. 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「SIC-POVM」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.