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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 Strong Subadditivity of Quantum Entropy ： ウィキペディア英語版 Strong Subadditivity of Quantum Entropy Strong subadditivity of entropy (SSA) was long known and appreciated in classical probability theory and information theory. Its extension to quantum mechanical entropy (the von Neumann entropy) was conjectured by D.W. Robinson and D. Ruelle 〔D. W. Robinson and D. Ruelle, Mean Entropy of States in Classical Statistical Mechanis, Communications in Mathematical Physics 5, 288 (1967)〕 in 1966 and O. E. Lanford III and D. W. Robinson 〔O. Lanford III, D. W. Robinson, Jour. Mathematical Physics, 9, 1120 (1968)〕 in 1968 and proved in 1973 by E.H. Lieb and M.B. Ruskai.〔E. H. Lieb, M. B. Ruskai, Proof of the Strong Subadditivity of Quantum Mechanichal Entropy, J. Math. Phys. 14, 1938–1941 (1973).〕 It is a basic theorem in modern quantum information theory. SSA concerns the relation between the entropies of various subsystems of a larger system consisting of three subsystems (or of one system with three degrees of freedom). The proof of this relation in the classical case is quite easy but the quantum case is difficult because of the non-commutativity of the density matrices describing the subsystems. Some useful references here are.〔M. Nielsen, I. Chuang Quantum Computation and Quantum Information, Cambr. U. Press, (2000)〕〔M. Ohya, D. Petz, Quantum Entropy and Its Use, Springer (1993)〕〔E. Carlen, Trace Inequalities and Quantum Entropy: An Introductory Course, Contemp. Math. 529 (2009).〕 ==Definitions== We will use the following notation throughout: A Hilbert space is denoted by $\backslash mathcal$, and $\backslash mathcal(\backslash mathcal)$ denotes the bounded linear operators on $\backslash mathcal$. Tensor products are denoted by superscripts, e.g., $\backslash mathcal^=\backslash mathcal^1\backslash otimes\; \backslash mathcal^2$. The trace is denoted by $$. 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「Strong Subadditivity of Quantum Entropy」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.