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Communications in Theoretical Physics

Remark on the One-Way Quantum Deficit for General Two-Qubit States

Lian-He Shao, Zhengjun Xi, Yongming Li

Published Mar 1, 2013• 5 citations
Publisher

Abstract

We reinvestigate the one-way quantum deficit, which is a measure of quantum correlation emerging from a thermodynamical approach. We give a tight upper bound of the one-way quantum deficit for general mixed states, and give a sufficient condition for this bound. Finally, we discuss a universal way to evaluate the one-way quantum deficit for general two-qubit states.

DOI
10.1088/0253-6102/59/3/07

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We reinvestigate the one-way quantum deficit, which is a measure of quantum correlation emerging from a thermodynamical approach. We give a tight upper bound of the one-way quantum deficit for general mixed states, and give a sufficient condition for this bound. Finally, we discuss a universal way to evaluate the one-way quantum deficit for general two-qubit states.
We introduce the concept of monogamy deficit for quantum correlation by combining two types of monogamy inequalities depending on different measurement sides. For tripartite pure states, we demonstrate a relation which connects two types of monogamy inequalities for quantum discord and provide the difference between them. By using this relation, we obtain a unified physical interpretation for these two monogamy deficits. In addition, we find the interesting fact that there is a general monogamy condition for several quantum correlations for tripartite pure states. We then provide a necessary and sufficient condition for the establishment of one kind of monogamy inequality for tripartite mixed states and generalize it to multipartite quantum states.
The work deficit, as introduced by Jonathan Oppenheim et al. [ Phys. Rev. Lett. 89 (2002) 180402 ] is a good measure of the quantum correlations in a state and provides a new standpoint for understanding quantum non-locality. In this paper, we analytically evaluate the one-way information deficit (OWID) for the Bell-diagonal states and a class of two-qubit states and further give the geometry picture for OWID. The dynamic behavior of the OWID under decoherence channel is investigated and it is shown that the OWID of some classes of X states is more robust against the decoherence than the entanglement.
Quantum deficit originates in questions regarding work extraction from quantum systems coupled to a heat bath [Phys. Rev. Lett. 89, 180402 (2002)]. It is a kind of quantum correlations besides entanglement and quantum discord, and links quantum thermodynamics with quantum correlations. In this paper, we evaluate the one-way deficit of two adjacent spins in the bulk for the XY model. We find that the one-way deficit characterizes the quantum phase transition in the XX model and the transverse field Ising model that the XY model reduces to for specified parameters. This study may enlighten extensive studies of quantum phase transitions from the perspective of quantum information and quantum correlations, including finite-temperature phase transitions, phase transitions of other quantum many-body models or even topological phase transitions.
The work deficit, as introduced by Jonathan Oppenheim et al. [Phys. Rev. Lett. 89 (2002) 180402] is a good measure of the quantum correlations in a state and provides a new standpoint for understanding quantum non-locality. In this paper, we analytically evaluate the one-way information deficit (OWID) for the Bell-diagonal states and a class of two-qubit states and further give the geometry picture for OWID. The dynamic behavior of the OWID under decoherence channel is investigated and it is shown that the OWID of some classes of X states is more robust against the decoherence than the entanglement.
So far, one-way information deficit (OWID) has been calculated explicitly only for Bell-diagonal states and the four-parameter family of X-states with additional assumptions and expressions for more general quantum states are not known. In this paper, we derive explicit expressions for OWID for a larger class of two-qubit states, namely, a five-parameter family of two-qubit states. The dynamic behavior of the OWID under decoherence channel is investigated and it is shown that the OWID is more robust against the decoherence than the entanglement.