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

摘要

We investigate the freezing phenomenon of quantum discord occurring in phase damping noise processes. Bynrelating the expression of the time variation of the discord to the convex function of relative entropy, we obtainnthe necessary and sufficient conditions of the phenomenon for standard Bell-diagonal states. These conditionsnare applicable also to the phenomenon occurring in a non-Markovian dephasing process. Moreover, we shownthat the same condition and phenomenon coincide in an unusual sort of Bell-diagonal states beyond the standardnform.