Categorical Equivalences from State-Effect Adjunctions

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

From every pair of adjoint functors it is possible to produce a (possibly trivial) equivalence of categories by restricting to the subcategories where the unit and counit are isomorphisms. If we do this for the adjunction between effect algebras and abstract convex sets, we get the surprising result that the equivalent subcategories consist of reflexive order-unit spaces and reflexive base-norm spaces, respectively. These are the convex sets that can occur as state spaces in generalized probabilistic theories satisfying both the no-restriction hypothesis and its dual. The linearity of the morphisms is automatic. If we add a compact topology to either the states or the effects, we can obtain a duality for all Banach order-unit spaces or all Banach base-norm spaces, but not both at the same time.
Original languageEnglish
Title of host publication5th International Conference on Quantum Physics and Logic, Canada, 3-7th June 2018
EditorsPeter Selinger, Giulio Chiribella
PublisherOpen Publishing Association
Pages107-126
Number of pages20
DOIs
Publication statusPublished - 31 Jan 2019
Event15th International Conference on Quantum Physics and Logic - Halifax, Canada
Duration: 3 Jun 20187 Jun 2018
https://www.mathstat.dal.ca/qpl2018/

Publication series

NameElectronic Proceedings in Theoretical Computer Science
PublisherOpen Publishing Association
Volume287
ISSN (Electronic)2075-2180

Conference

Conference15th International Conference on Quantum Physics and Logic
Abbreviated titleQPL 2018
CountryCanada
CityHalifax
Period3/06/187/06/18
Internet address

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