Categories of Quantum and Classical Channels (extended abstract)
We introduce the CP*–construction on a dagger compact closed category as a generalisation of Selinger's CPM-construction. While the latter takes a dagger compact closed category and forms its category of "abstract matrix algebras" and completely positive maps, the CP*-construction for...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Open Publishing Association
2014-07-01
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| Series: | Electronic Proceedings in Theoretical Computer Science |
| Online Access: | http://arxiv.org/pdf/1408.0049v1 |
| _version_ | 1818130502067945472 |
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| author | Bob Coecke Chris Heunen Aleks Kissinger |
| author_facet | Bob Coecke Chris Heunen Aleks Kissinger |
| author_sort | Bob Coecke |
| collection | DOAJ |
| description | We introduce the CP*–construction on a dagger compact closed category as a generalisation of Selinger's CPM-construction. While the latter takes a dagger compact closed category and forms its category of "abstract matrix algebras" and completely positive maps, the CP*-construction forms its category of "abstract C*-algebras" and completely positive maps. This analogy is justified by the case of finite-dimensional Hilbert spaces, where the CP*–construction yields the category of finite-dimensional C*-algebras and completely positive maps.
The CP*-construction fully embeds Selinger's CPM-construction in such a way that the objects in the image of the embedding can be thought of as "purely quantum" state spaces. It also embeds the category of classical stochastic maps, whose image consists of "purely classical" state spaces. By allowing classical and quantum data to coexist, this provides elegant abstract notions of preparation, measurement, and more general quantum channels. |
| first_indexed | 2024-12-11T08:06:03Z |
| format | Article |
| id | doaj.art-f9bef45e8c7841fb82eb05fe2475e487 |
| institution | Directory Open Access Journal |
| issn | 2075-2180 |
| language | English |
| last_indexed | 2024-12-11T08:06:03Z |
| publishDate | 2014-07-01 |
| publisher | Open Publishing Association |
| record_format | Article |
| series | Electronic Proceedings in Theoretical Computer Science |
| spelling | doaj.art-f9bef45e8c7841fb82eb05fe2475e4872022-12-22T01:14:59ZengOpen Publishing AssociationElectronic Proceedings in Theoretical Computer Science2075-21802014-07-01158Proc. QPL 201211410.4204/EPTCS.158.1:4Categories of Quantum and Classical Channels (extended abstract)Bob Coecke0Chris Heunen1Aleks Kissinger2 University of Oxford, Department of Computer Science University of Oxford, Department of Computer Science University of Oxford, Department of Computer Science We introduce the CP*–construction on a dagger compact closed category as a generalisation of Selinger's CPM-construction. While the latter takes a dagger compact closed category and forms its category of "abstract matrix algebras" and completely positive maps, the CP*-construction forms its category of "abstract C*-algebras" and completely positive maps. This analogy is justified by the case of finite-dimensional Hilbert spaces, where the CP*–construction yields the category of finite-dimensional C*-algebras and completely positive maps. The CP*-construction fully embeds Selinger's CPM-construction in such a way that the objects in the image of the embedding can be thought of as "purely quantum" state spaces. It also embeds the category of classical stochastic maps, whose image consists of "purely classical" state spaces. By allowing classical and quantum data to coexist, this provides elegant abstract notions of preparation, measurement, and more general quantum channels.http://arxiv.org/pdf/1408.0049v1 |
| spellingShingle | Bob Coecke Chris Heunen Aleks Kissinger Categories of Quantum and Classical Channels (extended abstract) Electronic Proceedings in Theoretical Computer Science |
| title | Categories of Quantum and Classical Channels (extended abstract) |
| title_full | Categories of Quantum and Classical Channels (extended abstract) |
| title_fullStr | Categories of Quantum and Classical Channels (extended abstract) |
| title_full_unstemmed | Categories of Quantum and Classical Channels (extended abstract) |
| title_short | Categories of Quantum and Classical Channels (extended abstract) |
| title_sort | categories of quantum and classical channels extended abstract |
| url | http://arxiv.org/pdf/1408.0049v1 |
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