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arXiv:quant-ph/0203007 · Journal of Modern Optics

Can there be quantum correlations in a mixture of two separable states?

Aditi Sen, Ujjwal Sen

Published Jan 1, 2003• 7 citations
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Abstract

We use a recently proposed measure of quantum correlations (work deficit) to measure the strength of the non-locality of an equal mixture of two bipartite orthogonal but locally indistinguishable separable states. This gives supporting evidence for a non-zero value of a separable state for this measure of non-locality. We show that a different order imposed on two states by the work deficit and any entanglement measure cannot be explained by mixedness alone.

DOI
10.1080/09500340308234547

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We use a recently proposed measure of quantum correlations (work deficit) to measure the strength of the non-locality of an equal mixture of two bipartite orthogonal but locally indistinguishable separable states. This gives supporting evidence for a non-zero value of a separable state for this measure of non-locality. We show that a different order imposed on two states by the work deficit and any entanglement measure cannot be explained by mixedness alone.
We consider the amount of work which can be extracted from a heat bath using a bipartite state rho\\rhorho shared by two parties. In general it is less then the amount of work extractable when one party is in possession of the entire state. We derive bounds for this "work deficit" and calculate it explicitly for a number of different cases. For pure states and maximally correlated states the work deficit is exactly equal to the distillable entanglement of the state. In these cases a form of complementarity exists between physical work which can be extracted and distillable entanglement. The work deficit is a good measure of the quantum correlations in a state and provides a new paradigm for understanding quantum non-locality.
We consider the amount of work which can be extracted from a heat bath using a bipartite state rho shared by two parties. In general it is less then the amount of work extractable when one party is in possession of the entire state. We derive bounds for this "work deficit" and calculate it explicitly for a number of different cases. In particuar, for pure states the work deficit is exactly equal to the distillable entanglement of the state. A form of complementarity exists between physical work which can be extracted and distillable entanglement. The work deficit is a good measure of the quantum correlations in a state and provides a new paradigm for understanding quantum nonlocality.
Quantum nonlocality is usually associated with entangled states by their violations of Bell-type inequalities. However, even unentangled systems, whose parts may have been prepared separately, can show nonlocal properties. In particular, a set of product states is said to exhibit "quantum nonlocality without entanglement" if the states are locally indistinguishable; i.e., it is not possible to optimally distinguish the states by any sequence of local operations and classical communication. Here, we present a stronger manifestation of this kind of nonlocality in multiparty systems through the notion of local irreducibility. A set of multiparty orthogonal quantum states is defined to be locally irreducible if it is not possible to locally eliminate one or more states from the set while preserving orthogonality of the postmeasurement states. Such a set, by definition, is locally indistinguishable, but we show that the converse does not always hold. We provide the first examples of orthogonal product bases on C^{d}⊗C^{d}⊗C^{d} for d=3, 4 that are locally irreducible in all bipartitions, where the construction for d=3 achieves the minimum dimension necessary for such product states to exist. The existence of such product bases implies that local implementation of a multiparty separable measurement may require entangled resources across all bipartitions.
Deficit of information zero-way was proposed in HorodeckiHHOSSS2005 as one of possible measures of quantumness of correlations. Numerical calculations suggested that there exist such states for which this quantity is almost equal to mutual information. In this paper we present a family of states for which we have equality between above measure of quantumness of correlations and the measure of total correlations -- mutual information. It means that whole correlations in these states have, in some sense, quantum character and that quantum correlations do not necessarily imply classical correlations. We prove this intriguing feature for a subclass of 2x2 separable states. We also present numerical result suggesting that this interesting situation might also happen for 2x2 entangled states.
We analyze a family of measures of general quantum correlations for composite systems, defined in terms of the bipartite entanglement necessarily created between systems and apparatuses during local measurements. For every entanglement monotone EEE, this operational correspondence provides a different measure QE{Q}_{E}QE​ of quantum correlations. Examples of such measures are the relative entropy of quantumness, the quantum deficit, and the negativity of quantumness. In general, we prove that any so-defined quantum correlation measure is always greater than (or equal to) the corresponding entanglement between the subsystems, ${Q}_{E}\ensuremath{\ge}E$, for arbitrary states of composite quantum systems. We analyze qualitatively and quantitatively the flow of correlations in iterated measurements, showing that general quantum correlations and entanglement can never decrease along von Neumann chains, and that genuine multipartite entanglement in the initial state of the observed system always gives rise to genuine multipartite entanglement among all subsystems and all measurement apparatuses at any level in the chain. Our results provide a comprehensive framework to understand and quantify general quantum correlations in multipartite states.
The presence of correlations among constituent quantum systems has great relevance in thermodynamics. Significant efforts have been devoted to investigate the role of correlations in work extraction, among others. Here we derive a bound on the difference between global and local extractable work by unitary operations (ergotropic gap) for bipartite separable states. Violation of this bound necessarily certifies the presence of entanglement. This gap is shown to be a monotone under local operations and classical communication-assisted state transformations for pure bipartite quantum states. Further, we provide a thermo-majorization criterion that is sufficient to compare the single-shot work deficit between two pure bipartite entangled states. The ergotropic gap has an implication in witnessing the dimension of a bipartite quantum state with the same local dimensions. On the other hand, our result gives an operational meaning to the Nielsen-Kempe disorder criterion. We also propose a schematic model to visualize the separability bound and to detect entanglement for a restricted class of quantum states.