Entropic bounds on information backflow

TL;DR

This paper establishes entropic bounds on information backflow in open quantum systems, linking quantum correlations and environmental changes to non-Markovian dynamics using telescopic relative entropy.

Contribution

It introduces bounds on entropic measures of information backflow, extending the understanding of non-Markovianity through a regularized quantum relative entropy.

Findings

Bounds are derived for telescopic relative entropy revivals.

Examples include Jaynes-Cummings model and two-qubit dynamics.

Results connect system-environment correlations to non-Markovian behavior.

Abstract

In the dynamics of open quantum systems, the backflow of information to the reduced system under study has been suggested as the actual physical mechanism inducing memory and thus leading to non-Markovian quantum dynamics. To this aim, the trace-distance or Bures-distance revivals between distinct evolved system states have been shown to be subordinated to the establishment of system-environment correlations or changes in the environmental state. We show that this interpretation can be substantiated also for a class of entropic quantifiers. We exploit a suitably regularized version of Umegaki's quantum relative entropy, known as telescopic relative entropy, that is tightly connected to the quantum Jensen-Shannon divergence. In particular, we derive general upper bounds on the telescopic relative entropy revivals conditioned and determined by the formation of correlations and changes in the environment. We illustrate our findings by means of examples, considering the Jaynes-Cummings model and a two-qubit dynamics.