Toy quantum categories (extended abstract)
<p>We show that Rob Spekken's toy quantum theory arises as an instance of our categorical approach to quantum axiomatics, as a (proper) subcategory of the dagger compact category <strong>FRel</strong> of finite sets and relations with the cartesian product as tensor, where obs...
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| Format: | Journal article |
| Language: | English |
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2011
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| _version_ | 1826283061833105408 |
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| author | Coecke, B Edwards, B |
| author_facet | Coecke, B Edwards, B |
| author_sort | Coecke, B |
| collection | OXFORD |
| description | <p>We show that Rob Spekken's toy quantum theory arises as an instance of our categorical approach to quantum axiomatics, as a (proper) subcategory of the dagger compact category <strong>FRel</strong> of finite sets and relations with the cartesian product as tensor, where observables correspond to dagger Frobenius algebras. This in particular implies that the quantum-like properties of the toy model are in fact very general categorytheoretic properties. We also show the remarkable fact that we can already interpret complementary quantum observables on the two-element set in <strong>FRel</strong>.</p> |
| first_indexed | 2024-03-07T00:53:15Z |
| format | Journal article |
| id | oxford-uuid:871dd12d-41cb-49dc-a5d9-d92f601008ef |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T00:53:15Z |
| publishDate | 2011 |
| record_format | dspace |
| spelling | oxford-uuid:871dd12d-41cb-49dc-a5d9-d92f601008ef2022-03-26T22:08:45ZToy quantum categories (extended abstract)Journal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:871dd12d-41cb-49dc-a5d9-d92f601008efComputingQuantum theory (mathematics)EnglishOxford University Research Archive - Valet2011Coecke, BEdwards, B<p>We show that Rob Spekken's toy quantum theory arises as an instance of our categorical approach to quantum axiomatics, as a (proper) subcategory of the dagger compact category <strong>FRel</strong> of finite sets and relations with the cartesian product as tensor, where observables correspond to dagger Frobenius algebras. This in particular implies that the quantum-like properties of the toy model are in fact very general categorytheoretic properties. We also show the remarkable fact that we can already interpret complementary quantum observables on the two-element set in <strong>FRel</strong>.</p> |
| spellingShingle | Computing Quantum theory (mathematics) Coecke, B Edwards, B Toy quantum categories (extended abstract) |
| title | Toy quantum categories (extended abstract) |
| title_full | Toy quantum categories (extended abstract) |
| title_fullStr | Toy quantum categories (extended abstract) |
| title_full_unstemmed | Toy quantum categories (extended abstract) |
| title_short | Toy quantum categories (extended abstract) |
| title_sort | toy quantum categories extended abstract |
| topic | Computing Quantum theory (mathematics) |
| work_keys_str_mv | AT coeckeb toyquantumcategoriesextendedabstract AT edwardsb toyquantumcategoriesextendedabstract |