Quantum Discord for Generalized Bloch Sphere States

TL;DR

This paper introduces an efficient method to analytically evaluate quantum discord for generalized Bloch sphere states in bipartite quantum systems, providing explicit formulas and a geometric interpretation.

Contribution

It presents a novel optimization procedure for calculating quantum discord and geometric quantum discord analytically for a broad class of bipartite states.

Findings

Derived an exact analytical formula for quantum discord of GBSS.

Developed an optimization method applicable to any concave entropy function.

Provided a geometric interpretation of quantum discord for these states.

Abstract

In this study for particular states of bipartite quantum system in 2n?2m dimensional Hilbert space state, similar to m or n-qubit density matrices represented in Bloch sphere we call them generalized Bloch sphere states(GBSS), we give an efficient optimization procedure so that analytic evaluation of quantum discord can be performed. Using this optimization procedure, we find an exact analytical formula for the optimum positive operator valued measure (POVM) that maximize the measure of the classical correlation for these states. The presented optimization procedure also is used to show that for any concave entropy function the same POVMs are sufficient for quantum discord of mentioned states. Furthermore, We show that such optimization procedure can be used to calculate the geometric measure of quantum discord (GMQD) and then an explicit formula for GMQD is given. Finally, a complete geometric view is presented for quantum discord of GBSS. Keywords: Quantum Discord, Generalized Bloch Sphere States, Dirac matrices, Bipartite Quantum System. PACs Index: 03.67.-a, 03.65.Ta, 03.65.Ud