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In quantum information theory, quantum discord is a measure of nonclassical correlations between two subsystems of a quantum system. It includes correlations that are due to quantum physical effects but do not necessarily involve quantum entanglement. The notion of quantum discord was introduced by Harold Ollivier and Wojciech H. Zurek〔Wojciech H. Zurek, ''Einselection and decoherence from an information theory perspective'', Annalen der Physik vol. 9, 855–864 (2000) (abstract )〕〔Harold Ollivier and Wojciech H. Zurek, ''Quantum Discord: A Measure of the Quantumness of Correlations'', Physics Review Letters vol. 88, 017901 (2001) (abstract )〕 and, independently by L. Henderson and Vlatko Vedral.〔L. Henderson and V. Vedral: ''Classical, quantum and total correlations'', Journal of Physics A 34, 6899 (2001), ()〕 Olliver and Zurek referred to it also as a measure of ''quantumness'' of correlations.〔 From the work of these two research groups it follows that quantum correlations can be present in certain mixed separable states;〔Paolo Giorda, Matteo G. A. Paris: ''Gaussian quantum discord'', quant-ph arXiv:1003.3207v2 (submitted on 16 Mar 2010, version of 22 March 2010) (p. 1 )〕 In other words, separability alone does not imply the absence of quantum effects. The notion of quantum discord thus goes beyond the distinction which had been made earlier between entangled versus separable (non-entangled) quantum states. == Definition and mathematical relations == In mathematical terms, quantum discord is defined in terms of the quantum mutual information. More specifically, quantum discord is the difference between two expressions which each, in the classical limit, represent the mutual information. These two expressions are: : : where, in the classical case, ''H''(''A'') is the information entropy, ''H''(''A'', ''B'') the joint entropy and ''H''(''A''|''B'') the conditional entropy, and the two expressions yield identical results. In the nonclassical case, the quantum physics analogy for the three terms are used – ''S''(''ρA'') the von Neumann entropy, ''S''(''ρ'') the joint quantum entropy and ''S''(''ρA''|''ρB'') the conditional quantum entropy, respectively, for probability density function ''ρ''; : : The difference between the two expressions (− ''JA''(''ρ'') ) defines the basis-dependent quantum discord, which is asymmetrical in the sense that can differ from .〔Borivoje Dakić, Vlatko Vedral, Caslav Brukner: ''Necessary and sufficient condition for nonzero quantum discord'', Phys. Rev. Lett., vol. 105, nr. 19, 190502 (2010), (arXiv:1004.0190v2 ) (submitted 1 April 2010, version of 3 November 2010)〕〔For a succinct overview see for ex (arXiv:0809.1723v2 )〕 The notation ''J'' represents the part of the correlations that can be attributed to classical correlations and varies in dependence on the chosen eigenbasis; therefore, in order for the quantum discord to reflect the purely nonclassical correlations independently of basis, it is necessary that ''J'' first be maximized over the set of all possible projective measurements onto the eigenbasis:〔For a more detailed overview see for ex. ''Signatures of nonclassicality in mixed-state quantum computation'', Physical Review A vol. 79, 042325 (2009), (arXiv:0811.4003 ) and see for ex. Wojciech H. Zurek: ''Decoherence and the transition from quantum to classical - revisited'', (p. 11 )〕 : Nonzero quantum discord indicates the presence of correlations that are due to noncommutativity of quantum operators.〔Shunlong Luo: ''Quantum discord for two-qubit systems'', Physical Review A, vol. 77, 042303 (2008) (abstract )〕 For pure states, the quantum discord becomes a measure of quantum entanglement,〔Animesh Datta, Anil Shaji, Carlton M. Caves: ''Quantum discord and the power of one qubit'', arXiv:0709.0548v1 (), 4 Sep 2007, (p. 4 )〕 more specifically, in that case it equals the entropy of entanglement.〔 Vanishing quantum discord is a criterion for the pointer states, which constitute preferred effectively classical states of a system.〔 It could be shown that quantum discord must be non-negative and that states with vanishing quantum discord can in fact be identified with pointer states.〔Animesh Datta: ''A condition for the nullity of quantum discord'', (arXiv:1003.5256v2 )〕 Other conditions have been identified which can be seen in analogy to the Peres–Horodecki criterion〔Bogna Bylicka, Dariusz Chru´sci´nski: ''Witnessing quantum discord in 2 x N systems'', arXiv:1004.0434v1 (), 3 April 2010〕 and in relation to the strong subadditivity of the von Neumann entropy.〔Vaibhav Madhok, Animesh Datta: ''Role of quantum discord in quantum communication'' (arXiv:1107.0994v1 ), (submitted 5 July 2011)〕 Efforts have been made to extend the definition of quantum discord to continuous variable systems, in particular to bipartite systems described by Gaussian states.〔C. Weedbrook, S. Pirandola, R. Garcia-Patron, N. J. Cerf, T. C. Ralph, J. H. Shapiro, S. Lloyd: ''Gaussian Quantum Information'', Reviews of Modern Physics 84, 621 (2012), available from arXiv:1110.3234v1 ()〕 A very recent work〔S. Pirandola, G. Spedalieri, S. L. Braunstein, N. J. Cerf, S. Lloyd: ''Optimality of Gaussian Discord'', Phys. Rev. Lett. 113, 140405 (2014), available from arXiv:1309.2215v3 (), 26 Nov 2014〕 has demonstrated that the upper-bound of Gaussian discord〔〔Gerardo Adesso, Animesh Datta: ''Quantum versus classical correlations in Gaussian states'', Phys. Rev. Lett. 105, 030501 (2010), available from arXiv:1003.4979v2 (), 15 July 2010〕 indeed coincides with the actual quantum discord of a Gaussian state, when the latter belongs to a suitable large family of Gaussian states. Computing quantum discord is NP-complete. Therefore, the running time of any algorithm for computing quantum discord is believed to grow exponentially with the dimension of the Hilbert space so that computing quantum discord in a quantum system of moderate size is not possible in practice. 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「quantum discord」の詳細全文を読む スポンサード リンク
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