New features of quantum discord uncovered by q-entropies

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 power-law 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 D_q for the q ne 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 D_q.