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Categorical equivalence between orthomodular dynamic algebras and complete orthomodular lattices

Abstract:
This paper provides a categorical equivalence between two types of quantum structures. One is a complete orthomodular lattice, which is used for reasoning about testable properties of a quantum system. The other is an orthomodular dynamic algebra, which is a quantale used for reasoning about quantum actions. The result extends to more restrictive lattices than orthomodular lattices, and includes Hilbert lattices of closed subspaces of a Hilbert space. These other lattice structures have connections to a wide range of different quantum structures; hence our equivalence establishes a categorical connection between quantales and a great variety of quantum structures.
Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s10773-017-3433-4

Authors

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Institution:
University of Oxford
Division:
Societies, Other & Subsidiary Companies
Department:
Kellogg College
Oxford college:
Kellogg College
Role:
Author

Publisher:
Springer
Journal:
International Journal of Theoretical Physics More from this journal
Volume:
56
Issue:
12
Pages:
4060–4072
Publication date:
2017-07-12
Acceptance date:
2017-05-25
DOI:
EISSN:
1572-9575
ISSN:
0020-7748

Keywords:
Pubs id:
pubs:698537
UUID:
uuid:7c9e9d7f-a150-4bda-9a45-bd5f3643334f
Local pid:
pubs:698537
Source identifiers:
698537
Deposit date:
2017-06-06

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