Framework for resource quantification in infinite-dimensional general probabilistic theories

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