  Resource theories provide a general framework for the characterization of
properties of physical systems in quantum mechanics and beyond. Here, we
introduce methods for the quantification of resources in general probabilistic
theories (GPTs), focusing in particular on the technical issues associated with
infinite-dimensional state spaces. We define a universal resource quantifier
based on the robustness measure, and show it to admit a direct operational
meaning: in any GPT, it quantifies the advantage that a given resource state
enables in channel discrimination tasks over all resourceless states. We show
that the robustness acts as a faithful and strongly monotonic measure in any
resource theory described by a convex and closed set of free states, and can be
computed through a convex conic optimization problem.
  Specializing to continuous-variable quantum mechanics, we obtain additional
bounds and relations, allowing an efficient computation of the measure and
comparison with other monotones. We demonstrate applications of the robustness
to several resources of physical relevance: optical nonclassicality,
entanglement, genuine non-Gaussianity, and coherence. In particular, we
establish exact expressions for various classes of states, including Fock
states and squeezed states in the resource theory of nonclassicality and
general pure states in the resource theory of entanglement, as well as tight
bounds applicable in general cases.
