Assessing non-Markovian dynamics

TL;DR

This paper develops criteria to determine if a quantum channel snapshot is consistent with Markovian dynamics, introduces a measure of Markovianity, and explores the geometry of quantum channels related to master equations.

Contribution

It provides the first computable necessary and sufficient criteria for assessing Markovianity of quantum channels from snapshots, without additional assumptions.

Findings

Criteria for Markovianity are computable and exact.

A new measure of Markovianity is introduced.

The geometry of quantum channels related to master equations is clarified.

Abstract

We investigate what a snapshot of a quantum evolution - a quantum channel reflecting open system dynamics - reveals about the underlying continuous time evolution. Remarkably, from such a snapshot, and without imposing additional assumptions, it can be decided whether or not a channel is consistent with a time (in)dependent Markovian evolution, for which we provide computable necessary and sufficient criteria. Based on these, a computable measure of `Markovianity' is introduced. We discuss how the consistency with Markovian dynamics can be checked in quantum process tomography. The results also clarify the geometry of the set of quantum channels with respect to being solutions of time (in)dependent master equations.