Operational Restrictions in General Probabilistic Theories
Abstract The formalism of general probabilistic theories provides a universal paradigm that is suitable for describing various physical systems including classical and quantum ones as particular cases. Contrary to the usual no-restriction hypothesis, the set of accessible meters within a given theor...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Filippov, Sergey N. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s) 2020 |
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| Übergeordnetes Werk: |
Enthalten in: Foundations of physics - Springer US, 1970, 50(2020), 8 vom: 12. Juli, Seite 850-876 |
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| Übergeordnetes Werk: |
volume:50 ; year:2020 ; number:8 ; day:12 ; month:07 ; pages:850-876 |
| Links: |
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| DOI / URN: |
10.1007/s10701-020-00352-6 |
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OLC211839876X |
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| 520 | |a Abstract The formalism of general probabilistic theories provides a universal paradigm that is suitable for describing various physical systems including classical and quantum ones as particular cases. Contrary to the usual no-restriction hypothesis, the set of accessible meters within a given theory can be limited for different reasons, and this raises a question of what restrictions on meters are operationally relevant. We argue that all operational restrictions must be closed under simulation, where the simulation scheme involves mixing and classical post-processing of meters. We distinguish three classes of such operational restrictions: restrictions on meters originating from restrictions on effects; restrictions on meters that do not restrict the set of effects in any way; and all other restrictions. We fully characterize the first class of restrictions and discuss its connection to convex effect subalgebras. We show that the restrictions belonging to the second class can impose severe physical limitations despite the fact that all effects are accessible, which takes place, e.g., in the unambiguous discrimination of pure quantum states via effectively dichotomic meters. We further demonstrate that there are physically meaningful restrictions that fall into the third class. The presented study of operational restrictions provides a better understanding on how accessible measurements modify general probabilistic theories and quantum theory in particular. | ||
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10.1007/s10701-020-00352-6 doi (DE-627)OLC211839876X (DE-He213)s10701-020-00352-6-p DE-627 ger DE-627 rakwb eng 570 530 VZ 11 12 5,21 ssgn Filippov, Sergey N. verfasserin (orcid)0000-0001-6414-2137 aut Operational Restrictions in General Probabilistic Theories 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2020 Abstract The formalism of general probabilistic theories provides a universal paradigm that is suitable for describing various physical systems including classical and quantum ones as particular cases. Contrary to the usual no-restriction hypothesis, the set of accessible meters within a given theory can be limited for different reasons, and this raises a question of what restrictions on meters are operationally relevant. We argue that all operational restrictions must be closed under simulation, where the simulation scheme involves mixing and classical post-processing of meters. We distinguish three classes of such operational restrictions: restrictions on meters originating from restrictions on effects; restrictions on meters that do not restrict the set of effects in any way; and all other restrictions. We fully characterize the first class of restrictions and discuss its connection to convex effect subalgebras. We show that the restrictions belonging to the second class can impose severe physical limitations despite the fact that all effects are accessible, which takes place, e.g., in the unambiguous discrimination of pure quantum states via effectively dichotomic meters. We further demonstrate that there are physically meaningful restrictions that fall into the third class. The presented study of operational restrictions provides a better understanding on how accessible measurements modify general probabilistic theories and quantum theory in particular. Quantum foundations General probabilistic theories Restrictions No-restriction hypothesis Measurement simulability Gudder, Stan aut Heinosaari, Teiko (orcid)0000-0003-2405-5439 aut Leppäjärvi, Leevi (orcid)0000-0002-9528-1583 aut Enthalten in Foundations of physics Springer US, 1970 50(2020), 8 vom: 12. Juli, Seite 850-876 (DE-627)130020907 (DE-600)421748-2 (DE-576)015562387 0015-9018 nnns volume:50 year:2020 number:8 day:12 month:07 pages:850-876 https://doi.org/10.1007/s10701-020-00352-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-AST SSG-OPC-AST GBV_ILN_22 AR 50 2020 8 12 07 850-876 |
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10.1007/s10701-020-00352-6 doi (DE-627)OLC211839876X (DE-He213)s10701-020-00352-6-p DE-627 ger DE-627 rakwb eng 570 530 VZ 11 12 5,21 ssgn Filippov, Sergey N. verfasserin (orcid)0000-0001-6414-2137 aut Operational Restrictions in General Probabilistic Theories 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2020 Abstract The formalism of general probabilistic theories provides a universal paradigm that is suitable for describing various physical systems including classical and quantum ones as particular cases. Contrary to the usual no-restriction hypothesis, the set of accessible meters within a given theory can be limited for different reasons, and this raises a question of what restrictions on meters are operationally relevant. We argue that all operational restrictions must be closed under simulation, where the simulation scheme involves mixing and classical post-processing of meters. We distinguish three classes of such operational restrictions: restrictions on meters originating from restrictions on effects; restrictions on meters that do not restrict the set of effects in any way; and all other restrictions. We fully characterize the first class of restrictions and discuss its connection to convex effect subalgebras. We show that the restrictions belonging to the second class can impose severe physical limitations despite the fact that all effects are accessible, which takes place, e.g., in the unambiguous discrimination of pure quantum states via effectively dichotomic meters. We further demonstrate that there are physically meaningful restrictions that fall into the third class. The presented study of operational restrictions provides a better understanding on how accessible measurements modify general probabilistic theories and quantum theory in particular. Quantum foundations General probabilistic theories Restrictions No-restriction hypothesis Measurement simulability Gudder, Stan aut Heinosaari, Teiko (orcid)0000-0003-2405-5439 aut Leppäjärvi, Leevi (orcid)0000-0002-9528-1583 aut Enthalten in Foundations of physics Springer US, 1970 50(2020), 8 vom: 12. Juli, Seite 850-876 (DE-627)130020907 (DE-600)421748-2 (DE-576)015562387 0015-9018 nnns volume:50 year:2020 number:8 day:12 month:07 pages:850-876 https://doi.org/10.1007/s10701-020-00352-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-AST SSG-OPC-AST GBV_ILN_22 AR 50 2020 8 12 07 850-876 |
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10.1007/s10701-020-00352-6 doi (DE-627)OLC211839876X (DE-He213)s10701-020-00352-6-p DE-627 ger DE-627 rakwb eng 570 530 VZ 11 12 5,21 ssgn Filippov, Sergey N. verfasserin (orcid)0000-0001-6414-2137 aut Operational Restrictions in General Probabilistic Theories 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2020 Abstract The formalism of general probabilistic theories provides a universal paradigm that is suitable for describing various physical systems including classical and quantum ones as particular cases. Contrary to the usual no-restriction hypothesis, the set of accessible meters within a given theory can be limited for different reasons, and this raises a question of what restrictions on meters are operationally relevant. We argue that all operational restrictions must be closed under simulation, where the simulation scheme involves mixing and classical post-processing of meters. We distinguish three classes of such operational restrictions: restrictions on meters originating from restrictions on effects; restrictions on meters that do not restrict the set of effects in any way; and all other restrictions. We fully characterize the first class of restrictions and discuss its connection to convex effect subalgebras. We show that the restrictions belonging to the second class can impose severe physical limitations despite the fact that all effects are accessible, which takes place, e.g., in the unambiguous discrimination of pure quantum states via effectively dichotomic meters. We further demonstrate that there are physically meaningful restrictions that fall into the third class. The presented study of operational restrictions provides a better understanding on how accessible measurements modify general probabilistic theories and quantum theory in particular. Quantum foundations General probabilistic theories Restrictions No-restriction hypothesis Measurement simulability Gudder, Stan aut Heinosaari, Teiko (orcid)0000-0003-2405-5439 aut Leppäjärvi, Leevi (orcid)0000-0002-9528-1583 aut Enthalten in Foundations of physics Springer US, 1970 50(2020), 8 vom: 12. Juli, Seite 850-876 (DE-627)130020907 (DE-600)421748-2 (DE-576)015562387 0015-9018 nnns volume:50 year:2020 number:8 day:12 month:07 pages:850-876 https://doi.org/10.1007/s10701-020-00352-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-AST SSG-OPC-AST GBV_ILN_22 AR 50 2020 8 12 07 850-876 |
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10.1007/s10701-020-00352-6 doi (DE-627)OLC211839876X (DE-He213)s10701-020-00352-6-p DE-627 ger DE-627 rakwb eng 570 530 VZ 11 12 5,21 ssgn Filippov, Sergey N. verfasserin (orcid)0000-0001-6414-2137 aut Operational Restrictions in General Probabilistic Theories 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Author(s) 2020 Abstract The formalism of general probabilistic theories provides a universal paradigm that is suitable for describing various physical systems including classical and quantum ones as particular cases. Contrary to the usual no-restriction hypothesis, the set of accessible meters within a given theory can be limited for different reasons, and this raises a question of what restrictions on meters are operationally relevant. We argue that all operational restrictions must be closed under simulation, where the simulation scheme involves mixing and classical post-processing of meters. We distinguish three classes of such operational restrictions: restrictions on meters originating from restrictions on effects; restrictions on meters that do not restrict the set of effects in any way; and all other restrictions. We fully characterize the first class of restrictions and discuss its connection to convex effect subalgebras. We show that the restrictions belonging to the second class can impose severe physical limitations despite the fact that all effects are accessible, which takes place, e.g., in the unambiguous discrimination of pure quantum states via effectively dichotomic meters. We further demonstrate that there are physically meaningful restrictions that fall into the third class. The presented study of operational restrictions provides a better understanding on how accessible measurements modify general probabilistic theories and quantum theory in particular. Quantum foundations General probabilistic theories Restrictions No-restriction hypothesis Measurement simulability Gudder, Stan aut Heinosaari, Teiko (orcid)0000-0003-2405-5439 aut Leppäjärvi, Leevi (orcid)0000-0002-9528-1583 aut Enthalten in Foundations of physics Springer US, 1970 50(2020), 8 vom: 12. Juli, Seite 850-876 (DE-627)130020907 (DE-600)421748-2 (DE-576)015562387 0015-9018 nnns volume:50 year:2020 number:8 day:12 month:07 pages:850-876 https://doi.org/10.1007/s10701-020-00352-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY SSG-OLC-AST SSG-OPC-AST GBV_ILN_22 AR 50 2020 8 12 07 850-876 |
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operational restrictions in general probabilistic theories |
| title_auth |
Operational Restrictions in General Probabilistic Theories |
| abstract |
Abstract The formalism of general probabilistic theories provides a universal paradigm that is suitable for describing various physical systems including classical and quantum ones as particular cases. Contrary to the usual no-restriction hypothesis, the set of accessible meters within a given theory can be limited for different reasons, and this raises a question of what restrictions on meters are operationally relevant. We argue that all operational restrictions must be closed under simulation, where the simulation scheme involves mixing and classical post-processing of meters. We distinguish three classes of such operational restrictions: restrictions on meters originating from restrictions on effects; restrictions on meters that do not restrict the set of effects in any way; and all other restrictions. We fully characterize the first class of restrictions and discuss its connection to convex effect subalgebras. We show that the restrictions belonging to the second class can impose severe physical limitations despite the fact that all effects are accessible, which takes place, e.g., in the unambiguous discrimination of pure quantum states via effectively dichotomic meters. We further demonstrate that there are physically meaningful restrictions that fall into the third class. The presented study of operational restrictions provides a better understanding on how accessible measurements modify general probabilistic theories and quantum theory in particular. © The Author(s) 2020 |
| abstractGer |
Abstract The formalism of general probabilistic theories provides a universal paradigm that is suitable for describing various physical systems including classical and quantum ones as particular cases. Contrary to the usual no-restriction hypothesis, the set of accessible meters within a given theory can be limited for different reasons, and this raises a question of what restrictions on meters are operationally relevant. We argue that all operational restrictions must be closed under simulation, where the simulation scheme involves mixing and classical post-processing of meters. We distinguish three classes of such operational restrictions: restrictions on meters originating from restrictions on effects; restrictions on meters that do not restrict the set of effects in any way; and all other restrictions. We fully characterize the first class of restrictions and discuss its connection to convex effect subalgebras. We show that the restrictions belonging to the second class can impose severe physical limitations despite the fact that all effects are accessible, which takes place, e.g., in the unambiguous discrimination of pure quantum states via effectively dichotomic meters. We further demonstrate that there are physically meaningful restrictions that fall into the third class. The presented study of operational restrictions provides a better understanding on how accessible measurements modify general probabilistic theories and quantum theory in particular. © The Author(s) 2020 |
| abstract_unstemmed |
Abstract The formalism of general probabilistic theories provides a universal paradigm that is suitable for describing various physical systems including classical and quantum ones as particular cases. Contrary to the usual no-restriction hypothesis, the set of accessible meters within a given theory can be limited for different reasons, and this raises a question of what restrictions on meters are operationally relevant. We argue that all operational restrictions must be closed under simulation, where the simulation scheme involves mixing and classical post-processing of meters. We distinguish three classes of such operational restrictions: restrictions on meters originating from restrictions on effects; restrictions on meters that do not restrict the set of effects in any way; and all other restrictions. We fully characterize the first class of restrictions and discuss its connection to convex effect subalgebras. We show that the restrictions belonging to the second class can impose severe physical limitations despite the fact that all effects are accessible, which takes place, e.g., in the unambiguous discrimination of pure quantum states via effectively dichotomic meters. We further demonstrate that there are physically meaningful restrictions that fall into the third class. The presented study of operational restrictions provides a better understanding on how accessible measurements modify general probabilistic theories and quantum theory in particular. © The Author(s) 2020 |
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| title_short |
Operational Restrictions in General Probabilistic Theories |
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https://doi.org/10.1007/s10701-020-00352-6 |
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| author2 |
Gudder, Stan Heinosaari, Teiko Leppäjärvi, Leevi |
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Gudder, Stan Heinosaari, Teiko Leppäjärvi, Leevi |
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| doi_str |
10.1007/s10701-020-00352-6 |
| up_date |
2024-07-03T19:10:01.667Z |
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