Geometric quantum discord with Bures distance

TL;DR

This paper introduces a new geometric measure of quantum correlations based on the Bures distance, linking quantum discord to state discrimination and entanglement for bipartite systems.

Contribution

It defines a Bures-distance-based quantum discord, connecting geometric quantum correlations with quantum state discrimination and entanglement measures.

Findings

The measure equals the success probability of an ambiguous quantum state discrimination task.

For pure states, it matches the geometric measure of entanglement.

Closest zero-discord states are characterized by optimal measurements.

Abstract

We define a new measure of quantum correlations in bipartite quantum systems given by the Bures distance of the system state to the set of classical states with respect to one subsystem, that is, to the states with zero quantum discord. Our measure is a geometrical version of the quantum discord. As the latter it quantifies the degree of non-classicality in the system. For pure states it is identical to the geometric measure of entanglement. We show that for mixed states it coincides with the optimal success probability of an ambiguous quantum state discrimination task. Moreover, the closest zero-discord states to a given state are obtained in terms of the corresponding optimal measurements.