Detecting initial system-environment correlations: Performance of various distance measures for quantum states

TL;DR

This paper compares four quantum state distance measures to evaluate their effectiveness in detecting initial system-environment correlations, revealing their strengths and limitations across different models.

Contribution

It provides a comprehensive analysis of multiple distance measures for identifying initial correlations, extending and correcting previous studies in the field.

Findings

Trace distance can increase due to initial correlations.

Bures metric, Hellinger distance, and Jensen-Shannon divergence also detect initial correlations.

Different measures have varying sensitivity depending on the model.

Abstract

We study the time evolution of four distance measures in the presence of initial systemenvironment correlations. It is well-known that the trace distance between two quantum states of an open system may increase due to initial correlations which leads to a breakdown of the contractivity of the reduced dynamics. Here we compare and analyze, for two different models, the time evolution of the trace distance, the Bures metric, the Hellinger distance and the Jensen-Shannon divergence regarding an increase above their initial values, witnessing initial correlations. This work generalizes, deepens and corrects the study performed by Dajka et al. [Phys. Rev. A 84 032120 (2011)] and thereby reveals generic features of the considered distance measures with respect to the capability of detecting initial system-environment correlations.