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 (or antidistinguishability) 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
characterization of the convex components and corresponding weights of such devices.
DOI: 10.1103/PhysRevLett.125.110402