Dynamical Memory Effects in Correlated Quantum Channels

TL;DR

This paper explores the relationship between two types of memory effects in quantum channels: correlations across multiple uses and non-Markovian dynamics during evolution, aiming to unify these concepts.

Contribution

It establishes a connection between correlated quantum channels and non-Markovian dynamics, integrating two distinct notions of memory in quantum systems.

Findings

Correlations between channel uses relate to non-Markovianity.

Non-divisibility of dynamical maps indicates non-Markovian behavior.

Unified framework for memory effects in quantum channels.

Abstract

Memory effects play a fundamental role in the study of the dynamics of open quantum systems. There exist two conceptually distinct notions of memory discussed for quantum channels in the literature. In quantum information theory quantum channels with memory are characterised by the existence of correlations between successive applications of the channel on a sequence of quantum systems. In open quantum systems theory memory effects arise dynamically during the time evolution of quantum systems, and define non-Markovian dynamics. Here we relate and combine these two different concepts of memory. In particular, we study the interplay between correlations between multiple uses of quantum channels and non-Markovianity as non-divisibility of the $t$-parametrized family of channels defining the dynamical map.