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Title: Framework for resource quantification in infinite-dimensional general probabilistic theories
Authors: Lami, Ludovico
Regula, Bartosz
Takagi, Ryuji
Ferrari, Giovanni
Keywords: Science::Physics
Issue Date: 2021
Source: Lami, L., Regula, B., Takagi, R. & Ferrari, G. (2021). Framework for resource quantification in infinite-dimensional general probabilistic theories. Physical Review A, 103(3), 032424-.
Project: NRF-NRFF2016-02
Journal: Physical Review A
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.
ISSN: 2469-9926
DOI: 10.1103/PhysRevA.103.032424
Rights: © 2021 American Physical Society (APS). Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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