Two roads to classicality
Mixing and decoherence are both manifestations of classicality within quantum theory, each of which admit a very general category-theoretic construction. We show under which conditions these two 'roads to classicality' coincide. This is indeed the case for (finite-dimensional) quantum theo...
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| Format: | Conference item |
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Electronic Proceedings in Theoretical Computer Science
2018
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| _version_ | 1797090773972287488 |
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| author | Coecke, B Selby, J Tull, S |
| author_facet | Coecke, B Selby, J Tull, S |
| author_sort | Coecke, B |
| collection | OXFORD |
| description | Mixing and decoherence are both manifestations of classicality within quantum theory, each of which admit a very general category-theoretic construction. We show under which conditions these two 'roads to classicality' coincide. This is indeed the case for (finite-dimensional) quantum theory, where each construction yields the category of C*-algebras and completely positive maps. We present counterexamples where the property fails which includes relational and modal theories. Finally, we provide a new interpretation for our category-theoretic generalisation of decoherence in terms of 'leaking information'. |
| first_indexed | 2024-03-07T03:23:32Z |
| format | Conference item |
| id | oxford-uuid:b8410b97-04fc-4981-8741-9f6dd9cb3d03 |
| institution | University of Oxford |
| last_indexed | 2024-03-07T03:23:32Z |
| publishDate | 2018 |
| publisher | Electronic Proceedings in Theoretical Computer Science |
| record_format | dspace |
| spelling | oxford-uuid:b8410b97-04fc-4981-8741-9f6dd9cb3d032022-03-27T04:54:35ZTwo roads to classicalityConference itemhttp://purl.org/coar/resource_type/c_5794uuid:b8410b97-04fc-4981-8741-9f6dd9cb3d03Symplectic Elements at OxfordElectronic Proceedings in Theoretical Computer Science2018Coecke, BSelby, JTull, SMixing and decoherence are both manifestations of classicality within quantum theory, each of which admit a very general category-theoretic construction. We show under which conditions these two 'roads to classicality' coincide. This is indeed the case for (finite-dimensional) quantum theory, where each construction yields the category of C*-algebras and completely positive maps. We present counterexamples where the property fails which includes relational and modal theories. Finally, we provide a new interpretation for our category-theoretic generalisation of decoherence in terms of 'leaking information'. |
| spellingShingle | Coecke, B Selby, J Tull, S Two roads to classicality |
| title | Two roads to classicality |
| title_full | Two roads to classicality |
| title_fullStr | Two roads to classicality |
| title_full_unstemmed | Two roads to classicality |
| title_short | Two roads to classicality |
| title_sort | two roads to classicality |
| work_keys_str_mv | AT coeckeb tworoadstoclassicality AT selbyj tworoadstoclassicality AT tulls tworoadstoclassicality |