Effect algebras, presheaves, non-locality and contextuality
Non-locality and contextuality are among the most counterintuitive aspects of quantum theory. They are difficult to study using classical logic and probability theory. In this paper we start with an effect algebraic approach to the study of non-locality and contextuality. We will see how different s...
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| Format: | Conference item |
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Springer
2015
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| _version_ | 1797102741297823744 |
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| author | Staton, S Uijlen, S |
| author_facet | Staton, S Uijlen, S |
| author_sort | Staton, S |
| collection | OXFORD |
| description | Non-locality and contextuality are among the most counterintuitive aspects of quantum theory. They are difficult to study using classical logic and probability theory. In this paper we start with an effect algebraic approach to the study of non-locality and contextuality. We will see how different slices over the category of set valued functors on the natural numbers induce different settings in which non-locality and contextuality can be studied. This includes the Bell, Hardy and Kochen-Specker-type paradoxes. We link this to earlier sheaf theoretic approaches by defining a fully faithful embedding of the category of effect algebras in this presheaf category over the natural numbers. |
| first_indexed | 2024-03-07T06:10:06Z |
| format | Conference item |
| id | oxford-uuid:ef2e06a6-b041-4988-8c79-daafbd5ad510 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T06:10:06Z |
| publishDate | 2015 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:ef2e06a6-b041-4988-8c79-daafbd5ad5102022-03-27T11:38:26ZEffect algebras, presheaves, non-locality and contextualityConference itemhttp://purl.org/coar/resource_type/c_c94fuuid:ef2e06a6-b041-4988-8c79-daafbd5ad510Symplectic Elements at OxfordSpringer2015Staton, SUijlen, SNon-locality and contextuality are among the most counterintuitive aspects of quantum theory. They are difficult to study using classical logic and probability theory. In this paper we start with an effect algebraic approach to the study of non-locality and contextuality. We will see how different slices over the category of set valued functors on the natural numbers induce different settings in which non-locality and contextuality can be studied. This includes the Bell, Hardy and Kochen-Specker-type paradoxes. We link this to earlier sheaf theoretic approaches by defining a fully faithful embedding of the category of effect algebras in this presheaf category over the natural numbers. |
| spellingShingle | Staton, S Uijlen, S Effect algebras, presheaves, non-locality and contextuality |
| title | Effect algebras, presheaves, non-locality and contextuality |
| title_full | Effect algebras, presheaves, non-locality and contextuality |
| title_fullStr | Effect algebras, presheaves, non-locality and contextuality |
| title_full_unstemmed | Effect algebras, presheaves, non-locality and contextuality |
| title_short | Effect algebras, presheaves, non-locality and contextuality |
| title_sort | effect algebras presheaves non locality and contextuality |
| work_keys_str_mv | AT statons effectalgebraspresheavesnonlocalityandcontextuality AT uijlens effectalgebraspresheavesnonlocalityandcontextuality |