Non-Markovianity and memory effects in quantum open systems

TL;DR

This paper introduces a new criterion and measure for quantum non-Markovianity that directly captures environmental memory effects, providing clearer physical interpretation than previous measures.

Contribution

It proposes a novel definition of non-Markovianity based on the inequality involving dynamical maps, distinct from divisibility-based measures, and demonstrates its effectiveness in quantum processes.

Findings

Nonzero memory effects exist even when other measures indicate Markovianity.

The new measure provides a physically interpretable criterion for quantum non-Markovianity.

The proposed definition is conceptually different from divisibility-based approaches.

Abstract

Although a number of measures for quantum non-Markovianity have been proposed recently, it is still an open question whether these measures directly characterize the memory effect of the environment, i.e., the dependence of a quantum state on its past in a time evolution. In this paper, we present a criterion and propose a measure for non-Markovianity with clear physical interpretations of the memory effect. The non-Markovianity is defined by the inequality $T(t_2,t_0)\neq T(t_2,t_1)T(t_1,t_0)$ in terms of memoryless dynamical map $T$ introduced in this paper. This definition is conceptually distinct from that based on divisibility used by Rivas et al (Phys. Rev. Lett 105, 050403 (2010)), whose violation is manifested by non-complete positivity of the dynamical map. We demonstrate via a typical quantum process that without Markovian approximation, nonzero memory effects (non-Markovianity) always exist even if the non-Markovianity is zero by the other non-Marovianity measures.