Dynamics of geometric and entropic quantifiers of correlations in open quantum systems

TL;DR

This paper compares geometric and entropic measures of correlations in open quantum systems, revealing qualitative differences especially in quantum discord dynamics, and discusses their implications for understanding quantum correlations.

Contribution

It introduces geometric quantifiers of total and classical correlations based on the Hilbert-Schmidt distance and compares their dynamics with entropic measures in a non-Markovian two-qubit system.

Findings

Qualitative differences occur only for quantum discord measures.

Geometric and entropic discords are not generally equivalent in dynamics.

Geometric and entropic total correlation quantifiers also show qualitative disagreements.

Abstract

We extend the Hilbert-Schmidt (square norm) distance, previously used to define the geometric quantum discord, to define also geometric quantifiers of total and classical correlations. We then compare the dynamics of geometric and entropic quantifiers of the different kinds of correlations in a non-Markovian open two-qubit system under local dephasing. We find that qualitative differences occur only for quantum discords. This is taken to imply that geometric and entropic discords are not, in general, equivalent in describing the dynamics of quantum correlations. We then show that also geometric and entropic quantifiers of total correlations present qualitative disagreements in the state space. This aspect indicates that the differences found for quantum discord are not attributable to a different separation, introduced by each measure, between the quantum and classical parts of correlations. Finally, we find that the Hilbert-Schmidt distance formally coincides with a symmetrized form of linear relative entropy.