Robustness of Coherence: An Operational and Observable Measure of Quantum Coherence

TLDR

Quantifying coherence is essential for quantum foundations and technologies. The authors define the robustness of coherence and prove it is a full monotone within recent resource theories of quantum coherence. They analytically evaluate the robustness on relevant state classes and provide an efficient semidefinite program for computing it on arbitrary states. The measure is observable as the expectation value of a coherence witness operator and quantifies the advantage a quantum state offers in phase‑discrimination tasks.

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.