Quantum non-Markovianity: characterization, quantification and detection

TLDR

This review surveys quantum non‑Markovianity, outlining its definitions, quantification methods, detection strategies, and highlighting open research questions. The authors define quantum Markovianity through divisibility, compare it with other criteria, and discuss proposals for quantifying and witnessing non‑Markovian dynamics.

Abstract

We present a comprehensive and up to date review on the concept of quantum non-Markovianity, a central theme in the theory of open quantum systems. We introduce the concept of quantum Markovian process as a generalization of the classical definition of Markovianity via the so-called divisibility property and relate this notion to the intuitive idea that links non-Markovianity with the persistence of memory effects. A detailed comparison with other definitions presented in the literature is provided. We then discuss several existing proposals to quantify the degree of non-Markovianity of quantum dynamics and to witness non-Markovian behavior, the latter providing sufficient conditions to detect deviations from strict Markovianity. Finally, we conclude by enumerating some timely open problems in the field and provide an outlook on possible research directions.