New features of quantum discord uncovered by -entropies

The notion of quantum discord introduced by Ollivier and Zurek [Phys. Rev. Lett 88 (2001) 017901] (see also Henderson and Vedral [J. Phys. A 34 (2001) 6899] ) 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 D 1 stand for the standard, Shannon-based discord measure and D q for the q ≠ 1 one. If two quantum states A , B are such that D 1 ( A ) > D 1 ( B ) , this order-relation does not remain invariant under a change from D 1 to D q .