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Categorical Equivalence Between Orthomodular Dynamic Algebras and Complete Orthomodular Lattices
Ist Teil von
International journal of theoretical physics, 2017-12, Vol.56 (12), p.4060-4072
Ort / Verlag
New York: Springer US
Erscheinungsjahr
2017
Link zum Volltext
Quelle
SpringerNature Journals
Beschreibungen/Notizen
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.