Geometric measure of quantum discord and the geometry of a class of two-qubit states

TL;DR

This paper explores the geometric structure of quantum entanglement and quantum discord in two-qubit X-states, analyzing their behavior under decoherence and establishing a law relating initial and evolved discord.

Contribution

It introduces a geometric visualization of quantum discord and entanglement for X-states and derives a factorization law for GMQD evolution under decoherence.

Findings

GMQD level surfaces are visualized geometrically.

Some initial states retain GMQD despite decoherence.

A factorization law links initial and final GMQD values.

Abstract

We investigate the geometric picture of the level surfaces of quantum entanglement and geometric measure of quantum discord (GMQD) of a class of X-states, respectively. This pictorial approach provides us a direct understanding of the structure of entanglement and GMQD. The dynamic evolution of GMQD under two typical kinds of quantum decoherence channels is also investigated. It is shown that there exists a class of initial states for which the GMQD is not destroyed by decoherence in a finite time interval. Furthermore, we establish a factorization law between the initial and final GMQD, which allows us to infer the evolution of entanglement under the influences of the environment.