Subtleties of witnessing quantum coherence in non-isolated systems

TL;DR

This paper extends a quantum coherence witness to non-isolated systems, revealing how environmental interactions affect quantum coherence detection and highlighting limitations of the Born approximation.

Contribution

It generalizes the No-Signalling-In-Time protocol to coupled systems, distinguishing different failure modes of the Born approximation in non-isolated quantum systems.

Findings

The protocol provides a lower bound on a coherence monotone.

It can detect system coherence and non-classical correlations.

It identifies failure modes of the Born approximation.

Abstract

Identifying non-classicality unambiguously and inexpensively is a long-standing open challenge in physics. The No-Signalling-In-Time protocol was developed as an experimental test for macroscopic realism, and serves as a witness of quantum coherence in isolated quantum systems by comparing the quantum state to its completely dephased counterpart. We show that it provides a lower bound on a certain resource-theoretic coherence monotone. We go on to generalise the protocol to the case where the system of interest is coupled to an environment. Depending on the manner of the generalisation, the resulting witness either reports on system coherence alone, or on a disjunction of system coherence with either (i) the existence of non-classical system-environment correlations or (ii) non-negligible dynamics in the environment. These are distinct failure modes of the Born approximation in non-isolated systems.