Necessary and sufficient conditions of freezing phenomena of quantum discord under phase damping

TL;DR

This paper derives the necessary and sufficient conditions for the freezing of quantum discord under phase damping noise, applicable to both Markovian and non-Markovian processes, and extends the phenomenon to a broader class of Bell-diagonal states.

Contribution

It provides a complete characterization of the freezing phenomenon of quantum discord for Bell-diagonal states under phase damping, including non-Markovian dynamics and generalized states.

Findings

Conditions for quantum discord freezing are explicitly derived.

Freezing phenomenon occurs in a broader class of Bell-diagonal states.

Results apply to both Markovian and non-Markovian phase damping processes.

Abstract

We investigate the freezing phenomenon of quantum discord occurring in phase damping noise processes. By relating the expression of the time variation of the discord to the convex function of relative entropy, we obtain the necessary and sufficient conditions of the phenomenon for standard Bell-diagonal states. These conditions are applicable also to the phenomenon occurring in a non-Markovian dephasing process. Moreover, we show that the same condition and phenomenon coincide in a new sort of Bell-diagonal states beyond the standard form.