Robustness of coherence: An operational and observable measure of quantum coherence

TL;DR

This paper introduces the robustness of coherence as a measurable and operationally meaningful quantifier of quantum coherence, applicable to various states and tasks in quantum information.

Contribution

It defines and proves the robustness of coherence as a full monotone, shows its observability via coherence witnesses, and provides an operational interpretation in phase discrimination.

Findings

Robustness of coherence is a full monotone in resource theory.

It can be measured as the expectation value of a witness operator.

Provides an efficient semidefinite program for computation.

Abstract

Quantifying coherence is an essential endeavour for both quantum foundations and quantum technologies. Here the robustness of coherence is defined and proven a full monotone in the context of the recently introduced resource theories of quantum coherence. The measure is shown to be observable, as it can be recast as the expectation value of a coherence witness operator for any quantum state. The robustness of coherence is evaluated analytically on relevant classes of states, and an efficient semidefinite program that computes it on general states is given. An operational interpretation is finally provided: the robustness of coherence quantifies the advantage enabled by a quantum state in a phase-discrimination task.