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理论物理通讯：英文版

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

王耀坤, Teng Ma, Bo Li, 王志玺

Published Jan 1, 2013• 0 citations
OpenAlex

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.

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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.
Recently Horodecki et al. [Phys. Rev. Lett. 90, 100402 (2003)] introduced an important quantum information processing paradigm in which two parties sharing many copies of the same bipartite quantum state distill local pure states by means of local unitary operations assisted by a one-way (two-way) completely dephasing channel. Local pure states are a valuable resource from a thermodynamical point of view since they allow thermal energy to be converted into work by local quantum heat engines. The work deficit was defined as the decrease in the work extractable from the joint system due to this process of localization, and was proposed as a measure of the quantumness of correlations. We give a simple information theoretical characterization of the one-way work deficit, which turns out to be complementary to a previously known operational measure of classical correlations, the one-way distillable common randomness
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.