Foundations and Measures of Quantum Non-Markovianity

TL;DR

This paper reviews recent advances in defining and measuring quantum non-Markovianity, emphasizing information flow, memory effects, and the role of system-environment correlations in open quantum system dynamics.

Contribution

It introduces a general mathematical framework and measures for quantum non-Markovianity based on information exchange and discusses methods to detect system-environment correlations.

Findings

A unified measure for quantum non-Markovianity based on information flow.

Methods to detect initial system-environment correlations via local measurements.

Analysis of the impact of correlations on non-Markovian dynamics.

Abstract

The basic features of the dynamics of open quantum systems, such as the dissipation of energy, the decay of coherences, the relaxation to an equilibrium or non-equilibrium stationary state, and the transport of excitations in complex structures are of central importance in many applications of quantum mechanics. The theoretical description, analysis and control of non-Markovian quantum processes play an important role in this context. While in a Markovian process an open system irretrievably loses information to its surroundings, non-Markovian processes feature a flow of information from the environment back to the open system, which implies the presence of memory effects and represents the key property of non-Markovian quantum behavior. Here, we review recent ideas developing a general mathematical definition for non-Markoviantiy in the quantum regime and a measure for the degree of memory effects in the dynamics of open systems which are based on the exchange of information between system and environment. We further study the dynamical effects induced by the presence of system-environment correlations in the total initial state and design suitable methods to detect such correlations through local measurements on the open system.