Categories of relations as models of quantum theory

Chris Heunen, Sean Tull

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


Categories of relations over a regular category form a family of models of quantum theory. Using regular logic, many properties of relations over sets lift to these models, including the correspondence between Frobenius structures and internal groupoids. Over compact Hausdorff spaces, this lifting gives continuous symmetric encryption. Over a regular Mal'cev category, this correspondence gives a characterization of categories of completely positive maps, enabling the formulation of quantum features. These models are closer to Hilbert spaces than relations over sets in several respects: Heisenberg uncertainty, impossibility of broadcasting, and behavedness of rank one morphisms.
Original languageEnglish
Title of host publicationProceedings 12th International Workshop on Quantum Physics and Logic
PublisherOpen Publishing Association
Number of pages15
Publication statusPublished - 2015

Publication series

NameElectronic Proceedings in Theoretical Computer Science
PublisherOpen Publishing Association

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