# Behavior of quantum correlations under nondissipative decoherence by means of the correlation matrix

## TL;DR

This paper investigates how quantum correlations, including quantum discord, behave under nondissipative decoherence using a correlation matrix approach, revealing that freezing of quantum discord does not always imply frozen quantum correlations.

## Contribution

The study introduces a correlation matrix method to analyze quantum correlations and demonstrates that quantum discord freezing does not necessarily correspond to frozen quantum correlations.

## Key findings

- Quantum discord can freeze without the actual quantum correlations freezing.
- The correlation matrix approach effectively distinguishes classical and quantum correlations.
- Quantum correlations may vary even when quantum discord remains constant.

## Abstract

In this paper we use 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. To illustrate the use of this matrix, we analyze the behavior of the correlations under non-dissipative decoherence in two-qubit states with maximally mixed marginals. 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 the Bell-diagonal states. In addition, we use the correlation matrix to study the phenomenon known as freezing of quantum discord. We find that under some initial conditions where freezing of quantum discord takes place, quantum correlation instead may remain not constant. In order to further explore into these results we also compute a non-commutativity measure of quantum correlations to analyze the behavior of quantum correlations under non-dissipative decoherence. 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.