Axiomatizing complete positivity
There are two ways to turn a categorical model for pure quantum theory into one for mixed quantum theory, both resulting in a category of completely positive maps. One has quantum systems as objects, whereas the other also allows classical systems on an equal footing. The former has been axiomatized...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Open Publishing Association
2015-11-01
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| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1506.02931v2 |
| _version_ | 1818424795336802304 |
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| author | Oscar Cunningham Chris Heunen |
| author_facet | Oscar Cunningham Chris Heunen |
| author_sort | Oscar Cunningham |
| collection | DOAJ |
| description | There are two ways to turn a categorical model for pure quantum theory into one for mixed quantum theory, both resulting in a category of completely positive maps. One has quantum systems as objects, whereas the other also allows classical systems on an equal footing. The former has been axiomatized using environment structures. We extend this axiomatization to the latter by introducing decoherence structures. |
| first_indexed | 2024-12-14T14:03:43Z |
| format | Article |
| id | doaj.art-f07a1c994551477e866c82989fc9cf7a |
| institution | Directory Open Access Journal |
| issn | 2075-2180 |
| language | English |
| last_indexed | 2024-12-14T14:03:43Z |
| publishDate | 2015-11-01 |
| publisher | Open Publishing Association |
| record_format | Article |
| series | Electronic Proceedings in Theoretical Computer Science |
| spelling | doaj.art-f07a1c994551477e866c82989fc9cf7a2022-12-21T22:58:40ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802015-11-01195Proc. QPL 201514815710.4204/EPTCS.195.11:69bAxiomatizing complete positivityOscar Cunningham0Chris Heunen1 University of Oxford University of Oxford There are two ways to turn a categorical model for pure quantum theory into one for mixed quantum theory, both resulting in a category of completely positive maps. One has quantum systems as objects, whereas the other also allows classical systems on an equal footing. The former has been axiomatized using environment structures. We extend this axiomatization to the latter by introducing decoherence structures.http://arxiv.org/pdf/1506.02931v2 |
| spellingShingle | Oscar Cunningham Chris Heunen Axiomatizing complete positivity Electronic Proceedings in Theoretical Computer Science |
| title | Axiomatizing complete positivity |
| title_full | Axiomatizing complete positivity |
| title_fullStr | Axiomatizing complete positivity |
| title_full_unstemmed | Axiomatizing complete positivity |
| title_short | Axiomatizing complete positivity |
| title_sort | axiomatizing complete positivity |
| url | http://arxiv.org/pdf/1506.02931v2 |
| work_keys_str_mv | AT oscarcunningham axiomatizingcompletepositivity AT chrisheunen axiomatizingcompletepositivity |