# Operational relevance of resource theories of quantum measurements

## TL;DR

This paper demonstrates that all resource measurements in convex resource theories provide an advantage in quantum state discrimination tasks and offers an operational interpretation of robustness as a measure of resource strength.

## Contribution

It establishes that every resource measurement offers advantage in discrimination tasks and links robustness to maximal relative advantage in these tasks.

## Key findings

- Resource measurements always offer advantage in state discrimination.
- Robustness quantifies the minimal noise to make a measurement free.
- Maximal advantage is characterized for incoherent and separable measurements.

## Abstract

For any resource theory it is essential to identify tasks for which resource objects offer advantage over free objects. We show that this identification can always be accomplished for resource theories of quantum measurements in which free objects form a convex subset of measurements on a given Hilbert space. To this aim we prove that every resource measurement offers advantage for some quantum state discrimination task. Moreover, we give an operational interpretation of robustness, which quantifies the minimal amount of noise that must be added to a measurement to make it free. Specifically, we show that this geometric quantity is related to the maximal relative advantage that a resource measurement offers in a class of minimal-error state discrimination problems. Finally, we apply our results to two classes of free measurements: incoherent measurements (measurements that are diagonal in the fixed basis) and separable measurements (measurements whose effects are separable operators). For both of these scenarios we find, in the asymptotic setting in which the dimension or the number of particles increase to infinity, the maximal relative advantage that resource measurements offer for state discrimination tasks.