New features of quantum discord uncovered by q-entropies

TL;DR

This paper extends the concept of quantum discord by incorporating q-entropies, revealing new non-classical correlation features and showing that the ordering of quantum states by discord can change with different entropy parameters.

Contribution

It introduces a generalized quantum discord based on q-entropies, highlighting differences from standard discord and exploring their implications for quantum correlations.

Findings

New discord-like measures describe different aspects of non-classicality.

Order relations between quantum states can change when using q-entropy-based discord.

Generalization reduces to standard discord as q approaches 1.

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 power-law q-entropies (that reduce to the standard Shannon entropy in the limit $q \to 1$) 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 $q \ne 1$ 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 $D_q$.