Coherence and non-classicality of quantum Markov processes

TL;DR

This paper establishes criteria to identify when quantum coherence indicates non-classicality in Markovian processes and shows that non-Markovian processes do not necessarily exhibit this connection.

Contribution

It provides a clear criterion linking quantum coherence to non-classicality in Markovian quantum processes and explores the differences in non-Markovian cases.

Findings

Markovian multi-time statistics cannot be classical if dynamics generate and convert coherences into populations

Quantum coherence is equivalent to non-classicality only in Markovian processes

Non-Markovian statistics may lack the connection between coherence and non-classicality

Abstract

Although quantum coherence is a basic trait of quantum mechanics, the presence of coherences in the quantum description of a certain phenomenon does not rule out the possibility to give an alternative description of the same phenomenon in purely classical terms. Here, we give definite criteria to determine when and to what extent quantum coherence is equivalent to non-classicality. We prove that a Markovian multi-time statistics obtained from repeated measurements of a non-degenerate observable cannot be traced back to a classical statistics if and only if the dynamics is able to generate coherences and to subsequently turn them into populations. Furthermore, we show with simple examples that such connection between quantum coherence and non-classicality is generally absent if the statistics is non-Markovian.