Conditions for the freezing phenomena of geometric measure of quantum discord for arbitrary two-qubit X states under non-dissipative dephasing noises

TL;DR

This paper identifies conditions under which the geometric measure of quantum discord remains unaffected during non-dissipative dephasing noises in arbitrary two-qubit X states, including non-Markovian processes.

Contribution

It provides necessary and sufficient conditions for the freezing of GMQD in two-qubit X states under phase damping noises, extending to non-Markovian environments.

Findings

GMQD remains unaffected under specific conditions

Conditions hold for both Markovian and non-Markovian dephasing

Results applicable to arbitrary two-qubit X states

Abstract

We study the dynamics of geometric measure of quantum discord (GMQD) under the influences of two local phase damping noises. Consider the two qubits initially in arbitrary X-states, we find the necessary and sufficient conditions for which GMQD is unaffected for a finite period. It is further shown that such results also hold for the non-Markovian dephasing process.