Assessing Non-Markovian Quantum Dynamics

TLDR

The study investigates what a single quantum channel snapshot reveals about the underlying continuous‑time evolution and how consistency with Markovian dynamics can be checked via quantum process tomography. The authors introduce a computable measure of Markovianity based on these criteria and discuss its application in quantum process tomography. They show that a snapshot alone suffices to determine whether a channel follows a time‑dependent or time‑independent Markovian evolution, providing necessary and sufficient criteria, and elucidate the geometry of the set of channels solvable by master equations.

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.