Revisiting the behavior of quantum correlations under nondissipative decoherence by means of the correlation matrix

Abstract

The main aim of this work is to investigate the relation between the freezing of Quantum Discord and the behavior of the actual quantum correlations present in bipartite quantum states. In order to accomplish this objective, we use first the Fano representation of two-qubit states from which we can identify a correlation matrix containing the information about the classical and quantum correlations present in the bipartite quantum state. From the behavior of the elements of the correlation matrix before and after making measurements on one of the subsystems, we identify the classical and quantum correlations present in these bipartite states. Then, we use this correlation matrix as a tool to analyze the phenomenon of non-dissipative decoherence in two-qubit states with maximally mixed marginals in typical dynamic scenarios where freezing of standard Quantum Discord takes place. We find that under some initial conditions where freezing of quantum discord occurs, some quantum correlations instead may not remain constant. In order to further explore into these results we also compute for the first time a recently introduced non-commutativity measure of quantum correlations (NCMQC) to analyze the behavior of quantum correlations under the same scenarios of non-dissipative decoherence. In complete agreement with the results obtained by means of the correlation matrix, our results also show that quantum correlations, as measured by NCMQC, do not freeze. Thus, our results put at stake the usual interpretation that the freezing of Quantum Discord is equivalent to the freezing of the physical quantum correlations themselves. We conclude from our study that freezing of quantum discord may not always be identified as equivalent to the freezing of the actual quantum correlations. Thus, the identification of freezing of quantum discord as a useful resource for tasks of quantum information processing is called into question.