New features of quantum discord uncovered by q-entropies

Abstract

The notion of quantum discord introduced by Ollivier and Zurek [Phys. Rev. Lett 88, 017901 (2001)] (see also Henderson and Vedral [J. Phys. A 34, 6899 (2001)]) has attracted increasing attention, in recent years, as an entropic quantifier of non-classical features pertaining to the correlations exhibited by bipartite quantum systems. Here we generalize the notion so as to encompass powerlaw q-entropies (that reduce to the standard Shannon entropy in the limit q → 1) and study the concomitant consequences. The ensuing, new discord-like measures we advance describe aspects of non-classicality that are different from those associated with the standard quantum discord. A particular manifestation of this difference concerns a feature related to order. Let D1 stand for the standard, Shannon-based discord measure and Dq for the q = 1 one. If two quantum states A, B are such that D1(A) > D1(B), this order-relation does not remain invariant under a change from D1 to Dq.

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“…The well known concurrence measure [53] is zero for separable states, and becomes one when maximal ignorance of each qubit state is achieved in the case of maximally entangled states. A non classical correlation measure known as the quantum discord [54][55][56] was shown to be non-zero even in non entangled states, and more recently, its q-entropies [57] was shown to incorporate aspects of non-classicality not visible within the conventional definition of the quantum discord.…”