Categorical Equivalence Between Orthomodular Dynamic Algebras and Complete Orthomodular Lattices

Kohei Kishida, Soroush Rafiee Rad, Joshua Sack, Shengyang Zhong

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)4060-4072
Number of pages13
JournalInternational Journal of Theoretical Physics
Volume56
Issue number12
DOIs
StatePublished - Dec 1 2017
Externally publishedYes

Keywords

  • Complete orthomodular lattice
  • Orthomodular dynamic algebra
  • Quantale

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy (miscellaneous)

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