翻訳と辞書 Words near each other ・ Channel X Radio ・ Channel Z ・ Channel Z (song) ・ Channel Zero ・ Channel Zero (band) ・ Channel Zero (comics) ・ Channel Zero (company) ・ Channel, California ・ Channel-associated signaling ・ Channel-billed cuckoo ・ Channel-billed toucan ・ Channel-conductance-controlling ATPase ・ Channel-inducing factor 4 ・ Channel-iron deposits ・ Channel-Port aux Basques ・ Channel-state duality ・ Channel-stopper ・ Channel-to-channel adapter ・ ChannelAdvisor ・ ChannelBee ・ Channeled pebblesnail ・ Channeled Scablands ・ Channeled whelk ・ ChannelFlip ・ ChannelGain ・ Channeling ・ Channeling the Quintessence of Satan ・ Channelization ・ Channelization (roads) ・ Channelization (telecommunications) Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Channel-state duality ： ウィキペディア英語版 Channel-state duality In quantum information theory, the channel-state duality refers to the correspondence between quantum channels and quantum states (described by density matrices). Phrased differently, the duality is the isomorphism between completely positive maps (channels) from ''A'' to C''n''×''n'', where ''A'' is a C *-algebra and C''n''×''n'' denotes the ''n''×''n'' complex entries, and positive linear functionals (states) on the tensor product :$\backslash mathbb^\; \backslash otimes\; A.$ ==Details== Let ''H''1 and ''H''2 be (finite-dimensional) Hilbert spaces. The family of linear operators acting on ''Hi'' will be denoted by ''L''(''Hi''). Consider two quantum systems, indexed by 1 and 2, whose states are density matrices in ''L''(''Hi'') respectively. A quantum channel, in the Schrödinger picture, is a completely positive (CP for short) linear map :$\backslash Phi\; :\; L(H\_1)\; \backslash rightarrow\; L(H\_2)$ that takes a state of system 1 to a state of system 2. Next we describe the dual state corresponding to Φ. Let ''Ei j'' denote the matrix unit whose ''ij''-th entry is 1 and zero elsewhere. The (operator) matrix :$\backslash rho\_\; =\; (\backslash Phi(E\_))\_\; \backslash in\; L(H\_1)\; \backslash otimes\; L(H\_2)$ is called the ''Choi matrix'' of Φ. By Choi's theorem on completely positive maps, Φ is CP if and only if ''ρ''Φ is positive (semidefinite). One can view ''ρ''Φ as a density matrix, and therefore the state dual to Φ. The duality between channels and states refers to the map :$\backslash Phi\; \backslash rightarrow\; \backslash rho\_,$ a linear bijection. This map is also called Jamiołkowski isomorphism or Choi–Jamiołkowski isomorphism. 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「Channel-state duality」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.