Operational theories and Categorical quantum mechanics
A central theme in current work in quantum information and quantum foundations is to see quantum mechanics as occupying one point in a space of possible theories, and to use this perspective to understand the special features and properties which single it out, and the possibilities for alternative...
| Principais autores: | , |
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| Formato: | Book section |
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Cambridge University Press
2016
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| _version_ | 1826272263447511040 |
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| author | Abramsky, S Heunen, C |
| author_facet | Abramsky, S Heunen, C |
| author_sort | Abramsky, S |
| collection | OXFORD |
| description | A central theme in current work in quantum information and quantum foundations is to see quantum mechanics as occupying one point in a space of possible theories, and to use this perspective to understand the special features and properties which single it out, and the possibilities for alternative theories. Two formalisms which have been used in this context are operational theories, and categorical quantum mechanics. The aim of the present paper is to establish strong connections between these two formalisms. We show how models of categorical quantum mechanics have representations as operational theories. We then show how nonlocality can be formulated at this level of generality, and study a number of examples from this point of view, including Hilbert spaces, sets and relations, and stochastic maps. The local, quantum, and no-signalling models are characterized in these terms. |
| first_indexed | 2024-03-06T22:09:47Z |
| format | Book section |
| id | oxford-uuid:5168f629-99d3-4a0c-a07e-7ed4db0efb4c |
| institution | University of Oxford |
| last_indexed | 2024-03-06T22:09:47Z |
| publishDate | 2016 |
| publisher | Cambridge University Press |
| record_format | dspace |
| spelling | oxford-uuid:5168f629-99d3-4a0c-a07e-7ed4db0efb4c2022-03-26T16:19:22ZOperational theories and Categorical quantum mechanicsBook sectionhttp://purl.org/coar/resource_type/c_3248uuid:5168f629-99d3-4a0c-a07e-7ed4db0efb4cSymplectic Elements at OxfordCambridge University Press2016Abramsky, SHeunen, CA central theme in current work in quantum information and quantum foundations is to see quantum mechanics as occupying one point in a space of possible theories, and to use this perspective to understand the special features and properties which single it out, and the possibilities for alternative theories. Two formalisms which have been used in this context are operational theories, and categorical quantum mechanics. The aim of the present paper is to establish strong connections between these two formalisms. We show how models of categorical quantum mechanics have representations as operational theories. We then show how nonlocality can be formulated at this level of generality, and study a number of examples from this point of view, including Hilbert spaces, sets and relations, and stochastic maps. The local, quantum, and no-signalling models are characterized in these terms. |
| spellingShingle | Abramsky, S Heunen, C Operational theories and Categorical quantum mechanics |
| title | Operational theories and Categorical quantum mechanics |
| title_full | Operational theories and Categorical quantum mechanics |
| title_fullStr | Operational theories and Categorical quantum mechanics |
| title_full_unstemmed | Operational theories and Categorical quantum mechanics |
| title_short | Operational theories and Categorical quantum mechanics |
| title_sort | operational theories and categorical quantum mechanics |
| work_keys_str_mv | AT abramskys operationaltheoriesandcategoricalquantummechanics AT heunenc operationaltheoriesandcategoricalquantummechanics |