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...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Language: | English |
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2021
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| Online Access: | https://hdl.handle.net/10356/151087 |
| _version_ | 1811687688310358016 |
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| author | Lami, Ludovico Regula, Bartosz Takagi, Ryuji Ferrari, Giovanni |
| author2 | School of Physical and Mathematical Sciences |
| author_facet | School of Physical and Mathematical Sciences Lami, Ludovico Regula, Bartosz Takagi, Ryuji Ferrari, Giovanni |
| author_sort | Lami, Ludovico |
| collection | NTU |
| description | 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. |
| first_indexed | 2024-10-01T05:20:17Z |
| format | Journal Article |
| id | ntu-10356/151087 |
| institution | Nanyang Technological University |
| language | English |
| last_indexed | 2024-10-01T05:20:17Z |
| publishDate | 2021 |
| record_format | dspace |
| spelling | ntu-10356/1510872023-02-28T19:49:02Z Framework for resource quantification in infinite-dimensional general probabilistic theories Lami, Ludovico Regula, Bartosz Takagi, Ryuji Ferrari, Giovanni School of Physical and Mathematical Sciences Science::Physics Quantum Foundations Quantum Information Processing With Continuous Variables 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. Ministry of Education (MOE) Nanyang Technological University National Research Foundation (NRF) Published version L.L. is supported by the ERC Synergy Grant BIOQ (Grant No. 319130) and by the Alexander von Humboldt Foundation. B.R. is supported by the Presidential Postdoctoral Fellowship from Nanyang Technological University, Singapore. R.T. acknowledges the support of NSF, ARO, IARPA, AFOSR, the Takenaka Scholarship Foundation, and the National Research Foundation (NRF) Singapore, under its NRFF Fellow programme (Award No. NRF-NRFF2016-02) and the Singapore Ministry of Education Tier 1 Grant No. 2019-T1-002-015. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the views of National Research Foundation, Singapore. G.F. acknowledges the support received from the EU through the ERASMUS+ Traineeship program and from the Scuola Galileiana di Studi Superiori. 2021-06-28T04:45:25Z 2021-06-28T04:45:25Z 2021 Journal Article 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-. https://dx.doi.org/10.1103/PhysRevA.103.032424 2469-9926 https://hdl.handle.net/10356/151087 10.1103/PhysRevA.103.032424 2-s2.0-85103136572 3 103 032424 en NRF-NRFF2016-02 2019-T1-002-015 Physical Review A © 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. application/pdf |
| spellingShingle | Science::Physics Quantum Foundations Quantum Information Processing With Continuous Variables Lami, Ludovico Regula, Bartosz Takagi, Ryuji Ferrari, Giovanni Framework for resource quantification in infinite-dimensional general probabilistic theories |
| title | Framework for resource quantification in infinite-dimensional general probabilistic theories |
| title_full | Framework for resource quantification in infinite-dimensional general probabilistic theories |
| title_fullStr | Framework for resource quantification in infinite-dimensional general probabilistic theories |
| title_full_unstemmed | Framework for resource quantification in infinite-dimensional general probabilistic theories |
| title_short | Framework for resource quantification in infinite-dimensional general probabilistic theories |
| title_sort | framework for resource quantification in infinite dimensional general probabilistic theories |
| topic | Science::Physics Quantum Foundations Quantum Information Processing With Continuous Variables |
| url | https://hdl.handle.net/10356/151087 |
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