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Quantifying coherence is an essential endeavour for both quantum foundationsand quantum technologies. Here the robustness of coherence is defined andproven a full monotone in the context of the recently introduced resourcetheories of quantum coherence. The measure is shown to be observable, as it canbe recast as the expectation value of a coherence witness operator for anyquantum state. The robustness of coherence is evaluated analytically onrelevant classes of states, and an efficient semidefinite program that computesit on general states is given. An operational interpretation is finallyprovided: the robustness of coherence quantifies the advantage enabled by aquantum state in a phase-discrimination task.

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