All quantum resources provide an advantage in exclusion tasks

TL;DR

This paper demonstrates that the convex weight measure of quantum resources precisely quantifies their advantage in exclusion tasks, linking resource quantification to operational performance across various quantum devices.

Contribution

It establishes that the convex weight measure has all key properties and directly corresponds to operational advantage in exclusion tasks for states, measurements, and transformations.

Findings

Convex weight equals the relative advantage in exclusion tasks.

Complete characterization of convex components for quantum devices.

Analytical bounds for convex weight of quantum resources.

Abstract

A key ingredient in quantum resource theories is a notion of measure. Such as a measure should have a number of fundamental properties, and desirably also a clear operational meaning. Here we show that a natural measure known as the convex weight, which quantifies the resource cost of a quantum device, has all the desired properties. In particular, the convex weight of any quantum resource corresponds exactly to the relative advantage it offers in an exclusion task. After presenting the general result, we show how the construction works for state assemblages, sets of measurements and sets of transformations. Moreover, in order to bound the convex weight analytically, we give a complete characterisation of the convex components and corresponding weights of such devices.