Enriched Quantales Arising from Complete Orthomodular Lattices

Studia Logica:1-39 (forthcoming)
  Copy   BIBTEX

Abstract

This paper connects complete orthomodular lattices to two enriched quantale structures. Complete orthomodular lattices emphasize a static perspective of a quantum system, helping us reason about testable properties of a quantum system. Quantales offer a dynamic perspective, helping us reason about the structure of quantum actions. We enrich quantales with an orthocomplementation-inducing operator, and call these structures orthomodular dynamic algebras. One type of orthomodular dynamic algebra distinguishes the joins of any two different sets of atoms, while the other distinguishes elements by the collective behavior of the atoms below it. We show that both orthomodular dynamic algebras are unital, and the unit is the top element of an induced orthomodular lattice. We provide a categorical equivalence between both orthomodular dynamic algebras and complete orthomodular lattices with isomorphisms, and we show that this equivalence is preserved when augmenting the orthomodular dynamic algebras with an involution. These equivalences help clarify the relationship between static and dynamic quantum structures.

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 94,659

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Analytics

Added to PP
2024-06-07

Downloads
8 (#1,360,066)

6 months
8 (#531,034)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Shengyang Zhong
Peking University

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references