Tight lower bound to the geometric measure of quantum discord

TL;DR

This paper establishes a rigorous lower bound for the geometric measure of quantum discord in bipartite states, improving upon previous bounds and providing a more accurate quantification of quantum correlations.

Contribution

It introduces a tighter lower bound for the geometric quantum discord in bipartite states, surpassing earlier bounds by Luo and Fu.

Findings

The new bound is strictly greater than previous bounds.

The bound applies to general bipartite quantum states.

It enhances the quantification of quantum correlations.

Abstract

Dakic, Vedral and Brukner [Physical Review Letters \tf{105},190502 (2010)] gave a geometric measure of quantum discord in a bipartite quantum state as the distance of the state from the closest classical quantum (or zero discord) state and derived an explicit formula for a two qubit state. Further, S.Luo and S.Fu [Physical Review A \tf{82}, 034302 (2010)] obtained a generic form of this geometric measure for a general bipartite state and established a lower bound. In this brief report we obtain a rigorous lower bound to the geometric measure of quantum discord in a general bipartite state which dominates that obtained by S.Luo and S.Fu.