The Bundle-Theoretic Structure and Computational Modeling of Quantum Contextuality

We propose a novel mathematical framework, rooted in fiber bundle theory, to quantify the phenomenon of quantum contextuality—a fundamental aspect of quantum entanglement. To demonstrate its utility, we first apply the formalism to quantum models in the foundations of quantum physics that both captu...

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Detalhes bibliográficos
Autores: Sahil, I., Merelli, E., Rodrigues, S.
Formato: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2025
País:España
Recursos:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/2088
Acesso em linha:http://hdl.handle.net/20.500.11824/2088
Access Level:acceso abierto
Palavra-chave:non-locality and contextuality
models of computation
fiber bundle theory
algebraic topology
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spelling The Bundle-Theoretic Structure and Computational Modeling of Quantum ContextualitySahil, I.Merelli, E.Rodrigues, S.non-locality and contextualitymodels of computationfiber bundle theoryalgebraic topologyWe propose a novel mathematical framework, rooted in fiber bundle theory, to quantify the phenomenon of quantum contextuality—a fundamental aspect of quantum entanglement. To demonstrate its utility, we first apply the formalism to quantum models in the foundations of quantum physics that both capture and differentiate varying strengths of contextuality. By revealing the intrinsic geometric structure of contextuality, the framework establishes a direct link to its computational foundations, facilitating the formulation of a topology-based model of computation that encapsulates the semantics inherent to contextuality. The framework delivers a rigorous and potentially more profound mathematical characterization of quantum contextuality, while offering new modeling methodologies for quantum cognition.PID2023-146683OB-100 funded by MICIU/AEI /10.13039/501100011033 and by ERDF, EU202520252025info:eu-repo/semantics/articleinfo:eu-repo/semantics/acceptedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/2088reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Inglésinfo:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2022-2025Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/openAccessoai:bird.bcamath.org:20.500.11824/20882026-06-19T12:47:47Z
dc.title.none.fl_str_mv The Bundle-Theoretic Structure and Computational Modeling of Quantum Contextuality
title The Bundle-Theoretic Structure and Computational Modeling of Quantum Contextuality
spellingShingle The Bundle-Theoretic Structure and Computational Modeling of Quantum Contextuality
Sahil, I.
non-locality and contextuality
models of computation
fiber bundle theory
algebraic topology
title_short The Bundle-Theoretic Structure and Computational Modeling of Quantum Contextuality
title_full The Bundle-Theoretic Structure and Computational Modeling of Quantum Contextuality
title_fullStr The Bundle-Theoretic Structure and Computational Modeling of Quantum Contextuality
title_full_unstemmed The Bundle-Theoretic Structure and Computational Modeling of Quantum Contextuality
title_sort The Bundle-Theoretic Structure and Computational Modeling of Quantum Contextuality
dc.creator.none.fl_str_mv Sahil, I.
Merelli, E.
Rodrigues, S.
author Sahil, I.
author_facet Sahil, I.
Merelli, E.
Rodrigues, S.
author_role author
author2 Merelli, E.
Rodrigues, S.
author2_role author
author
dc.subject.none.fl_str_mv non-locality and contextuality
models of computation
fiber bundle theory
algebraic topology
topic non-locality and contextuality
models of computation
fiber bundle theory
algebraic topology
description We propose a novel mathematical framework, rooted in fiber bundle theory, to quantify the phenomenon of quantum contextuality—a fundamental aspect of quantum entanglement. To demonstrate its utility, we first apply the formalism to quantum models in the foundations of quantum physics that both capture and differentiate varying strengths of contextuality. By revealing the intrinsic geometric structure of contextuality, the framework establishes a direct link to its computational foundations, facilitating the formulation of a topology-based model of computation that encapsulates the semantics inherent to contextuality. The framework delivers a rigorous and potentially more profound mathematical characterization of quantum contextuality, while offering new modeling methodologies for quantum cognition.
publishDate 2025
dc.date.none.fl_str_mv 2025
2025
2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/2088
url http://hdl.handle.net/20.500.11824/2088
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2022-2025
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
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instname:Basque Center for Applied Mathematics (BCAM)
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reponame_str BIRD. BCAM's Institutional Repository Data
collection BIRD. BCAM's Institutional Repository Data
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