Operational Markov condition for quantum processes

TL;DR

This paper establishes a comprehensive criterion for quantum Markovian processes, unifying previous definitions and introducing measures of non-Markovianity with practical operational meanings.

Contribution

It presents a necessary and sufficient condition for quantum Markovianity that aligns with classical cases and introduces operational measures of non-Markovianity.

Findings

Unified quantum Markov condition covering all known definitions

Derived measures of non-Markovianity with operational interpretations

Applicable to experimental testing of Markovian hypotheses

Abstract

We derive a necessary and sufficient condition for a quantum process to be Markovian which coincides with the classical one in the relevant limit. Our condition unifies all previously known definitions for quantum Markov processes by accounting for all potentially detectable memory effects. We then derive a family of measures of non-Markovianity with clear operational interpretations, such as the size of the memory required to simulate a process, or the experimental falsifiability of a Markovian hypothesis.