Framework for resource quantification in infinite-dimensional general probabilistic theories

TL;DR

This paper develops a universal resource quantification method for infinite-dimensional general probabilistic theories, with applications to quantum resources like entanglement and nonclassicality, providing operational meaning and computational tools.

Contribution

It introduces a robustness-based resource measure for GPTs, applicable to infinite dimensions, with operational interpretation and computational methods, extending resource theories to continuous-variable quantum systems.

Findings

Robustness measure quantifies resource advantage in channel discrimination.

The measure is convex, strongly monotonic, and computable via convex optimization.

Applications include bounds and exact expressions for nonclassicality, entanglement, and non-Gaussianity.

Abstract

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.