Categories of Empirical Models
A notion of morphism that is suitable for the sheaf-theoretic approach to contextuality is developed, resulting in a resource theory for contextuality. The key features involve using an underlying relation rather than a function between measurement scenarios, and allowing for stochastic mappings of...
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| Format: | Article |
| Language: | English |
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Open Publishing Association
2019-01-01
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| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1804.01514v3 |
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doaj-91df248d673a4522a37f6fff091ccbcb2020-11-24T21:43:28ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802019-01-01287Proc. QPL 201823925210.4204/EPTCS.287.14:16Categories of Empirical ModelsMartti Karvonen0 University of Edinburgh A notion of morphism that is suitable for the sheaf-theoretic approach to contextuality is developed, resulting in a resource theory for contextuality. The key features involve using an underlying relation rather than a function between measurement scenarios, and allowing for stochastic mappings of outcomes to outcomes. This formalizes an intuitive idea of using one empirical model to simulate another one with the help of pre-shared classical randomness. This allows one to reinterpret concepts and earlier results in terms of morphisms. Most notably: non-contextual models are precisely those allowing a morphism from the terminal object; contextual fraction is functorial; Graham-reductions induce morphisms, reinterpreting Vorob'evs theorem; contextual models cannot be cloned.http://arxiv.org/pdf/1804.01514v3 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Martti Karvonen |
| spellingShingle |
Martti Karvonen Categories of Empirical Models Electronic Proceedings in Theoretical Computer Science |
| author_facet |
Martti Karvonen |
| author_sort |
Martti Karvonen |
| title |
Categories of Empirical Models |
| title_short |
Categories of Empirical Models |
| title_full |
Categories of Empirical Models |
| title_fullStr |
Categories of Empirical Models |
| title_full_unstemmed |
Categories of Empirical Models |
| title_sort |
categories of empirical models |
| publisher |
Open Publishing Association |
| series |
Electronic Proceedings in Theoretical Computer Science |
| issn |
2075-2180 |
| publishDate |
2019-01-01 |
| description |
A notion of morphism that is suitable for the sheaf-theoretic approach to contextuality is developed, resulting in a resource theory for contextuality. The key features involve using an underlying relation rather than a function between measurement scenarios, and allowing for stochastic mappings of outcomes to outcomes. This formalizes an intuitive idea of using one empirical model to simulate another one with the help of pre-shared classical randomness. This allows one to reinterpret concepts and earlier results in terms of morphisms. Most notably: non-contextual models are precisely those allowing a morphism from the terminal object; contextual fraction is functorial; Graham-reductions induce morphisms, reinterpreting Vorob'evs theorem; contextual models cannot be cloned. |
| url |
http://arxiv.org/pdf/1804.01514v3 |
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AT marttikarvonen categoriesofempiricalmodels |
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