Geometric measure of quantum discord over two-sided projective measurements

TL;DR

This paper introduces a geometric measure of quantum discord for bipartite states considering two-sided projective measurements, extending previous one-sided measures and providing simplified formulas and bounds.

Contribution

It extends the geometric measure of quantum discord to two-sided projective measurements with explicit formulas and bounds, enhancing understanding of quantum correlations.

Findings

Derived a simplified expression for the new measure.

Established a lower bound for the geometric measure.

Obtained explicit formulas for special cases.

Abstract

The original definition of quantum discord of bipartite states was defined over one-sided projective measurements, it describes quantum correlation more extensively than entanglement. Dakic, Vedral, and Brukner [Phys. Rev. Lett. 105 (2010) 190502] introduced a geometric measure for this quantum discord, and Luo, Fu [Phys. Rev. A 82 (2010) 034302] simplified the variation expression of it. In this paper we introduce a geometric measure for the quantum discord over two-sided projective measurements. A simplified expression and a lower bound of this geometric measure are derived and explicit expressions are obtained for some special cases.