Quantifying coherence of quantum measurements

TL;DR

This paper develops a resource theory framework to quantify the coherence of quantum measurements, introduces a new coherence monotone, and demonstrates its experimental assessment on a quantum processor.

Contribution

It establishes a resource theoretical approach to measurement coherence, introduces a new coherence monotone based on POVM elements, and proposes an experimental scheme for measurement coherence quantification.

Findings

The coherence monotone provides a lower bound on measurement robustness.

The proposed scheme can be experimentally implemented on IBM Q.

Measurement coherence offers an operational advantage in state discrimination.

Abstract

In this work we investigate how to quantify the coherence of quantum measurements. First, we establish a resource theoretical framework to address the coherence of measurement and show that any statistical distance can be adopted to define a coherence monotone of measurement. For instance, the relative entropy fulfills all the required properties as a proper monotone. We specifically introduce a coherence monotone of measurement in terms of off-diagonal elements of Positive-Operator-Valued Measure (POVM) components. This quantification provides a lower bound on the robustness of measurement-coherence that has an operational meaning as the maximal advantage over all incoherent measurements in state discrimination tasks. Finally, we propose an experimental scheme to assess our quantification of measurement-coherence and demonstrate it by performing an experiment using a single qubit on IBM Q processor.