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Chinese Physics Letters

Quantum Correlations in a Family of Bipartite Qubit-Qutrit Separable States

Biao‐Liang Ye, Yimin Liu, Xiansong Liu, Zhanjun Zhang

Published Feb 1, 2013• 12 citations
Publisher

Abstract

Quantum correlations in a family of bipartite separable qubit-qutrit quantum-classical correlated states are investigated by using two popular measures, i.e., the original quantum discord (OQD) method by Ollivier and Zurek [ Phys. Rev. Lett. 88 (2001) 017901 ] and the measurement-induced disturbance (MID) method by Luo [ Phys. Rev. A 77 (2008) 022301 ]. It is found that both of them are functions of a parameter partially characterizing the concerned states, however, quantum correlations evaluated via the convenient MID method are somewhat overestimated.

DOI
10.1088/0256-307x/30/2/020302

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Quantum correlations in a family of bipartite separable qubit-qutrit quantum-classical correlated states are investigated by using two popular measures, i.e., the original quantum discord (OQD) method by Ollivier and Zurek [ Phys. Rev. Lett. 88 (2001) 017901 ] and the measurement-induced disturbance (MID) method by Luo [ Phys. Rev. A 77 (2008) 022301 ]. It is found that both of them are functions of a parameter partially characterizing the concerned states, however, quantum correlations evaluated via the convenient MID method are somewhat overestimated.
Quantum correlations in a family of two-qubit separable classical-quantum correlated states are intensively studied with four different approaches, namely, quantum discord [Phys. Rev. Lett. 88 (2002) 017901], measurement-induced disturbance (MID) [ Phys. Rev. A 77 (2008) 022301 ], ameliorated MID [ J. Phys. A: Math. Theor. 44 (2011) 352002 ] and quantum dissonance [ Phys. Rev. Lett. 104 (2010) 080501 ]. Quantum correlations captured with different approaches are compared and discussed so that their three distinct features are exposed.
Measure-induced non-classicality( MINC) in a family of bipartite separable qubit-qutrit correlated states was evaluated by using the MID method proposed by the reference [Luo S L. Using measurement-induced disturbance to characterize correlations as classical or quantum[J]. Phys Rev A,2008,77: 022301]. Specifically,classical correlation in each state was derived via the spectrum resolution technique and then the MINC( i. e.,quantum correlation) was extracted. The MINC was amply analyzed so that some distinct features were exposed.
Quantum discord, as introduced by Olliver and Zurek [Phys. Rev. Lett. 88, 017901 (2001)], is a measure of the discrepancy between two natural yet different quantum analogs of the classical mutual information. This notion characterizes and quantifies quantumness of correlations in bipartite states from a measurement perspective, and is fundamentally different from the various entanglement measures in the entanglement vs separability paradigm. The phenomenon of nonzero quantum discord is a manifestation of quantum correlations due to noncommutativity rather than due to entanglement, and has interesting and significant applications in revealing the advantage of certain quantum tasks. We will evaluate analytically the quantum discord for a large family of two-qubit states, and make a comparative study of the relationships between classical and quantum correlations in terms of the quantum discord. We furthermore compare the quantum discord with the entanglement of formation, and illustrate that the latter may be larger than the former, although for separable states, the entanglement of formation always vanishes and thus is less than the quantum discord.
Abstract In this study, the qubit quantum correlation swapping (QCS) is generalized to the qutrit case. To be concrete, two qutrit Werner states are taken as the research objects and the complete set of qutrit Bell states are utilized as the intermediate two-qutrit measure to implement QCS. The popular quantum correlation measure, i.e. quantum discord (Ollivier and Zurek 2001 Phys. Rev. Lett. 88 017901), is employed to characterize and quantify quantum correlations in the concerned states. The properties of the variance and threshold of quantum correlations occurring in the swapping process are revealed, and two distinct QCS phenomena are thus observed. Moreover, it is found that the maximal amount of quantum correlations in the final state can not exceed the minimal one of these in the initial states.
In [S. L. Luo, Using measurement induced disturbance to characterize correlations as classical or quantum, Phys. Rev. A77 (2008) 022301], the author presented a statistical correlation measure for bipartite quantum states using measurement induced disturbance. In this paper, motivated by this correlation measure, we obtain some necessary conditions for [Formula: see text]-classical states in multipartite quantum systems, and obtain a relation between the set of [Formula: see text]-classical states and the set of [Formula: see text]-product states; Secondly, we introduce a class of correlation measures based on trace distance using measurement induced disturbance in order to quantify the strength of correlation for non-[Formula: see text]-classical states; Lastly, we introduce the concept of quantum channel with respect to [Formula: see text]-partition, it is simply denoted by identical-[Formula: see text]-channel, and furthermore discuss the influences of the correlation measure under identical-[Formula: see text]-channel.
Quantum discord, a kind of quantum correlation, is defined as the difference between quantum mutual information and classical correlation in a bipartite system. In general, this correlation is different from entanglement, and quantum discord may be nonzero even for certain separable states. Even in the simple case of bipartite quantum systems, this different kind of quantum correlation has interesting and significant applications in quantum information processing. So far, quantum discord has been calculated explicitly only for a rather limited set of two-qubit quantum states and expressions for more general quantum states are not known. In this article, we derive explicit expressions for quantum discord for a larger class of two-qubit states, namely, a seven-parameter family of so called XXX states that have been of interest in a variety of contexts in the field. We also study the relation between quantum discord, classical correlation, and entanglement for a number of two-qubit states to demonstrate that they are independent measures of correlation with no simple relative ordering between them.