A classical appraisal of quantum definitions of non-Markovian dynamics

TL;DR

This paper compares classical and quantum definitions of non-Markovian dynamics, analyzing quantum measures of non-Markovianity derived from classical process signatures, and explores quantum dynamics built from classical processes.

Contribution

It provides a detailed analysis of quantum non-Markovianity measures based on classical process signatures, clarifying their relation and applicability.

Findings

Quantum non-Markovianity measures relate to classical process signatures.

Certain classical signatures of non-Markovianity have quantum counterparts.

Analysis of quantum dynamics derived from classical processes enhances understanding of non-Markovian behavior.

Abstract

We consider the issue of non-Markovianity of a quantum dynamics starting from a comparison with the classical definition of Markovian process. We point to the fact that two sufficient but not necessary signatures of non-Markovianity of a classical process find their natural quantum counterpart in recently introduced measures of quantum non-Markovianity. This behavior is analyzed in detail for quantum dynamics which can be built taking as input a class of classical processes.