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arXiv:1208.0879 · Communications in Theoretical Physics

One-Way Information Deficit and Geometry for a Class of Two-Qubit States

Yaokun Wang, Teng Ma, Bo Li, Zhi‐Xi Wang

Published May 1, 2013• 17 citations
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Abstract

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.

DOI
10.1088/0253-6102/59/5/04

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arXiv:quant-ph/0410090•Physical Review A•Jun 9, 2005•448 citations
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.
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.
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.
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.
In spite of many results in quantum information theory, the complex nature of compound systems is far from clear. In general the information is a mixture of local and nonlocal (``quantum'') information. It is important from both pragmatic and theoretical points of view to know the relationships between the two components. To make this point more clear, we develop and investigate the quantum-information processing paradigm in which parties sharing a multipartite state distill local information. The amount of information which is lost because the parties must use a classical communication channel is the deficit. This scheme can be viewed as complementary to the notion of distilling entanglement. After reviewing the paradigm in detail, we show that the upper bound for the deficit is given by the relative entropy distance to so-called pseudoclassically correlated states; the lower bound is the relative entropy of entanglement. This implies, in particular, that any entangled state is informationally nonlocal---i.e., has nonzero deficit. We also apply the paradigm to defining the thermodynamical cost of erasing entanglement. We show the cost is bounded from below by relative entropy of entanglement. We demonstrate the existence of several other nonlocal phenomena which can be found using the paradigm of local information. For example, we prove the existence of a form of nonlocality without entanglement and with distinguishability. We analyze the deficit for several classes of multipartite pure states and obtain that in contrast to the GHZ state, the Aharonov state is extremely nonlocal. We also show that there do not exist states for which the deficit is strictly equal to the whole informational content (bound local information). We discuss the relation of the paradigm with measures of classical correlations introduced earlier. It is also proved that in the one-way scenario, the deficit is additive for Bell diagonal states. We then discuss complementary features of information in distributed quantum systems. Finally we discuss the physical and theoretical meaning of the results and pose many open questions.