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arXiv:1307.6660 · Journal of Physics A Mathematical and Theoretical

One-way unlocalizable information deficit

Xue‐Na Zhu, Shao-Ming Fei

Published Jul 24, 2013• 2 citations
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Abstract

We introduce a one-way unlocalizable information deficit with respect to the one-way information deficit, similar to the definition of one-way unlocalizable quantum discord with respect to one-way quantum discord. The properties of the one-way unlocalizable information deficit and the relations among one-way unlocalizable information deficit, one-way unlocalizable quantum discord, one-way quantum discord, one-way information deficit and other quantum correlations are investigated. Analytical formulas of the one-way unlocalizable information deficit are given with detailed examples.

DOI
10.1088/1751-8113/46/32/325303

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We introduce a one-way unlocalizable information deficit with respect to the one-way information deficit, similar to the definition of one-way unlocalizable quantum discord with respect to one-way quantum discord. The properties of the one-way unlocalizable information deficit and the relations among one-way unlocalizable information deficit, one-way unlocalizable quantum discord, one-way quantum discord, one-way information deficit and other quantum correlations are investigated. Analytical formulas of the one-way unlocalizable information deficit are given with detailed examples.
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We relate the problem of irreversibility of entanglement with the recently defined measures of quantum correlation--quantum discord and one-way quantum deficit. We show that the entanglement of formation is always strictly larger than the coherent information and the entanglement cost is also larger in most cases. We prove irreversibility of entanglement under local operations and classical communication for a family of entangled states. This family is a generalization of the maximally correlated states for which we also give an analytic expression for the distillable entanglement, the relative entropy of entanglement, the distillable secret key, and the quantum discord.
Criteria of measure quantifying quantum coherence, a unique property of quantum system, are proposed recently. In this paper, we first give an uncertainty-like expression relating the coherence and the entropy of quantum system. This finding allows us to discuss the relations between the entanglement and the coherence. Further, we discuss in detail the relations among the coherence, the discord and the deficit in the bipartite quantum system. We show that, the one-way quantum deficit is equal to the sum between quantum discord and the relative entropy of coherence of measured subsystem.
We examine the behavior of quantum correlations of spin pairs in a finite anisotropic XY spin chain immersed in a transverse magnetic field, through the analysis of the quantum discord and the conventional and quadratic one way-information deficits. We first provide a brief review of these measures, showing that the last ones can be obtained as particular cases of a generalized information deficit based on general entropic forms. All these measures coincide with an entanglement entropy in the case of pure states, but can be non-zero in separable mixed states, vanishing just for classically correlated states. It is then shown that their behavior in the exact ground state of the chain exhibits similar features, deviating significantly from that of the pair entanglement below the critical field. In contrast with entanglement, they reach full range in this region, becoming independent of the pair separation and coupling range in the immediate vicinity of the factorizing field. It is also shown, however, that significant differences between the quantum discord and the information deficits arise in the local minimizing measurement that defines them. Both analytical and numerical results are provided.
We examine the behavior of quantum correlations of spin pairs in a finite anisotropic XY spin chain immersed in a transverse magnetic field, through the analysis of the quantum discord and the conventional and quadratic one-way information deficits. We first provide a brief review of these measures, showing that the last ones can be obtained as particular cases of a generalized information deficit based on general entropic forms. All of these measures coincide with an entanglement entropy in the case of pure states, but can be non-zero in separable mixed states, vanishing just for classically correlated states. It is then shown that their behavior in the exact ground state of the chain exhibits similar features, deviating significantly from that of the pair entanglement below the critical field. In contrast with entanglement, they reach full range in this region, becoming independent of the pair separation and coupling range in the immediate vicinity of the factorizing field. It is also shown, however, that significant differences between the quantum discord and the information deficits arise in the local minimizing measurement that defines them. Both analytical and numerical results are provided.