Framework for resource quantification in infinite-dimensional general probabilistic theories

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.

Automated summary

Resource theories provide a framework for characterizing properties of physical systems, with a universal resource quantifier based on robustness. It can be used to quantify resources in general probabilistic theories and is computed through convex conic optimization problems. The robustness acts as a faithful and strongly monotonic measure in resource theories described by convex and closed sets of free states, and has applications in various physical resources such as optical nonclassicality, entanglement, non-Gaussianity, and coherence.