翻訳と辞書 Words near each other ・ Mutual, Maryland ・ Mutual, Ohio ・ Mutual, Oklahoma ・ Mutual-benefit nonprofit corporation ・ MutualArt.com ・ Mutualism ・ Mutualism (biology) ・ Mutualism (economic theory) ・ Mutualism (movement) ・ Mutualisms and conservation ・ Mutualista ・ Mutuality ・ Mutualization ・ Mutually Assured Destruction (The Americans) ・ Mutually protected occlusion ・ Mutually unbiased bases ・ Mutuals' Deferred Shares Act 2015 ・ Mutuelleville ・ Mutukan ・ Mutukula ・ Mutukula Airport ・ Mutukula, Tanzania ・ Mutukula, Uganda ・ Mutula Kilonzo ・ Mutuli ・ Mutulia ・ Mutulu Shakur ・ Mutum ・ Mutum River ・ Mutum River (Amapá) 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 Mutually unbiased bases ： ウィキペディア英語版 Mutually unbiased bases In quantum information theory, mutually unbiased bases in Hilbert space C''d'' are two orthonormal bases $\backslash$ and $\backslash$ such that the square of the magnitude of the inner product between any basis states $|e\_j\backslash rangle$ and $|f\_k\backslash rangle$ equals the inverse of the dimension ''d'':〔I. Bengtsson, Three ways to look at mutually unbiased bases, http://arxiv.org/abs/quant-ph/0610216.〕 :$|\backslash langle\; e\_j|f\_k\; \backslash rangle|^2\; =\; \backslash frac,\; \backslash quad\; \backslash forall\; j,k\; \backslash in\; \backslash .$ These bases are ''unbiased'' in the following sense: if a system is prepared in a state belonging to one of the bases, then all outcomes of the measurement with respect to the other basis will occur with equal probabilities. == Overview == The notion of mutually unbiased bases was first introduced by Schwinger in 1960,〔J. Schwinger, "Unitary Operator Bases, Harvard University, 1960, http://www.pubmedcentral.nih.gov/picrender.fcgi?artid=222876&blobtype=pdf.〕 and the first person to consider applications of mutually unbiased bases was Ivanovic in the problem of quantum state determination. Another area where mutually unbiased bases can be applied is quantum key distribution, more specifically in secure quantum key exchange.〔M. Planat et al, A Survey of Finite Algebraic Geometrical Structures Underlying Mutually Unbiased Quantum Measurements, http://hal.ccsd.cnrs.fr/docs/00/07/99/18/PDF/MUB_FP.pdf.〕 Mutually unbiased bases are used in many protocols since the outcome is random when a measurement is made in a basis unbiased to that in which the state was prepared. When two remote parties share two non-orthogonal quantum states, attempts by an eavesdropper to distinguish between these by measurements will affect the system and this can be detected. While many quantum cryptography protocols have relied on 1-qubit technologies, employing higher-dimensional states, such as qutrits, allows for better security against eavesdropping.〔 This motivates the study of mutually unbiased bases in higher-dimensional spaces. Other uses of mutually unbiased bases include quantum state reconstruction, quantum error correction codes, detection of quantum entanglement, and the so-called "mean king's problem". 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「Mutually unbiased bases」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.