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.
Original language | English (US) |
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Pages (from-to) | 4060-4072 |
Number of pages | 13 |
Journal | International Journal of Theoretical Physics |
Volume | 56 |
Issue number | 12 |
DOIs | |
State | Published - Dec 1 2017 |
Externally published | Yes |
Keywords
- Complete orthomodular lattice
- Orthomodular dynamic algebra
- Quantale
ASJC Scopus subject areas
- General Mathematics
- Physics and Astronomy (miscellaneous)