  Resource theories can be used to formalize the quantification and
manipulation of resources in quantum information processing such as
entanglement, asymmetry and coherence of quantum states, and incompatibility of
quantum measurements. Given a certain state or measurement, one can ask whether
there is a task in which it performs better than any resourceless state or
measurement. Using conic programming, we prove that any general robustness
measure (with respect to a convex set of free states or measurements) can be
seen as a quantifier of such outperformance in some discrimination task. We
apply the technique to various examples, e.g. joint measurability, POVMs
simulable by projective measurements, and state assemblages preparable with a
given Schmidt number.
