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.
Highlights
The success of quantum mechanics in fields such as computation, communication, and information processing owes to the fact that certain properties of quantum systems, dubbed resources, can be exploited to enable significant advantages over purely classical methods in practical tasks
Previous works on resources in infinite-dimensional quantum mechanics are limited to the restricted Gaussian framework [33,34] or make strong technical assumptions such as compactness of the relevant sets [16]. This prevents us from being able to use them in the description of some of the most fundamental physical settings, such as quantum optical systems or general probabilistic theories (GPTs) in general Banach spaces
In this work we develop a general method of quantifying resources in infinite dimensions, applicable both to quantum mechanics and broader GPTs, and directly connected with the performance advantage in practical tasks
Summary
The success of quantum mechanics in fields such as computation, communication, and information processing owes to the fact that certain properties of quantum systems, dubbed resources, can be exploited to enable significant advantages over purely classical methods in practical tasks. Previous works on resources in infinite-dimensional quantum mechanics are limited to the restricted Gaussian framework [33,34] or make strong technical assumptions such as compactness of the relevant sets [16] This prevents us from being able to use them in the description of some of the most fundamental physical settings, such as quantum optical systems or GPTs in general Banach spaces. We introduce a variant of the robustness applicable to infinite-dimensional theories and show that it directly quantifies the maximal advantage that a given state provides in a family of channel discrimination tasks This extends from the finite-dimensional cases a deep connection between resource quantification and the fundamental operational tasks of discrimination.
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