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arXiv:1103.4032 · Physical Review Letters

All Nonclassical Correlations Can Be Activated into Distillable Entanglement

Marco Piani, Sevag Gharibian, Gerardo Adesso, John Calsamiglia, Paweł Horodecki, Andreas Winter

Published Jun 3, 2011• 250 citations
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Abstract

We devise a protocol in which general nonclassical multipartite correlations produce a physically relevant effect, leading to the creation of bipartite entanglement. In particular, we show that the relative entropy of quantumness, which measures all nonclassical correlations among subsystems of a quantum system, is equivalent to and can be operationally interpreted as the minimum distillable entanglement generated between the system and local ancillae in our protocol. We emphasize the key role of state mixedness in maximizing nonclassicality: Mixed entangled states can be arbitrarily more nonclassical than separable and pure entangled states.

DOI
10.1103/physrevlett.106.220403

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We devise a protocol in which general nonclassical multipartite correlations produce a physically relevant effect, leading to the creation of bipartite entanglement. In particular, we show that the relative entropy of quantumness, which measures all nonclassical correlations among subsystems of a quantum system, is equivalent to and can be operationally interpreted as the minimum distillable entanglement generated between the system and local ancillae in our protocol. We emphasize the key role of state mixedness in maximizing nonclassicality: Mixed entangled states can be arbitrarily more nonclassical than separable and pure entangled states.
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We study quantum coarse-grained entropy and demonstrate that the gap in entropy between local and global coarse-grainings is a natural generalization of entanglement entropy to mixed states and multipartite systems. This ``quantum correlation entropy'' Sqc{S}^{q}cSqc is additive over independent systems, is invariant under local unitary operations, measures total nonclassical correlations (vanishing on states with strictly classical correlation), and reduces to the entanglement entropy for bipartite pure states. It quantifies how well a quantum system can be understood via local measurements and ties directly to nonequilibrium thermodynamics, including representing a lower bound on the quantum part of thermodynamic entropy production. We discuss two other measures of nonclassical correlation to which this entropy is equivalent and argue that together they provide a unique thermodynamically distinguished measure.
We analyze the general nonclassicality of correlations of a composite quantum system as measured by the negativity of quantumness. The latter corresponds to the minimum entanglement, as quantified by the negativity that is created between the system and an apparatus that is performing local measurements on a selection of subsystems. The negativity of quantumness thus quantifies the degree of nonclassicality on the measured subsystems. We demonstrate a number of possible different interpretations for this measure and for the concept of quantumness of correlations in general. In particular, for general bipartite states in which the measured subsystem is a qubit, the negativity of quantumness acquires a geometric interpretation as the minimum trace distance from the set of classically correlated states. This can be further reinterpreted as minimum disturbance, with respect to trace norm, due to a local measurement or a nontrivial local unitary operation. We calculate the negativity of quantumness in closed form for Werner and isotropic states and for all two-qubit states for which the reduced state of the system that is locally measured is maximally mixed; this includes all Bell diagonal states. We discuss the operational significance and potential role of the negativity of quantumness in quantum information processing.
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We propose a general measure of nonclassical correlations for bipartite systems based on generalized entropic functions and majorization properties. Defined as the minimum information loss due to a local measurement, in the case of pure states it reduces to the generalized entanglement entropy, i.e., the generalized entropy of the reduced state. However, in the case of mixed states it can be nonzero in separable states, vanishing just for states diagonal in a general product basis, like the quantum discord. Simple quadratic measures of quantum correlations arise as a particular case of the present formalism. The minimum information loss due to a joint local measurement is also discussed. The evaluation of these measures in simple relevant cases is as well provided, together with comparison with the corresponding entanglement monotones.