Ontological models for quantum theory as functors

Alexandru Gheorghiu, Chris Heunen

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

Abstract

We interpret ontological models for finite-dimensional quantum theory as functors from the category of finite-dimensional C*-algebras and completely positive maps to the category of measurable spaces and Markov kernels. This uniformises several earlier results, that we analyse more closely: Pusey, Barrett, and Rudolph's result rules out monoidal functors; Leifer and Maroney's result rules out functors that preserve a duality between states and measurement; Aaronson et al's result rules out functors that adhere to the Schrodinger equation. We also prove that it is possible to have epistemic functors that take values in signed Markov kernels.
Original languageEnglish
Title of host publicationProceedings 16th International Conference on Quantum Physics and Logic
Subtitle of host publicationChapman University, Orange, CA, USA., 10-14 June 2019
EditorsBob Coecke, Mathew Leifer
PublisherOpen Publishing Association
Pages196-212
Number of pages17
DOIs
Publication statusPublished - 1 May 2020
EventQuantum Physics and Logic 2019 - Orange, United States
Duration: 10 Jun 201914 Jun 2019
https://qpl2019.org/

Publication series

NameElectronic Proceedings in Theoretical Computer Science
PublisherOpen Publishing Association
Volume318
ISSN (Electronic)2075-2180

Conference

ConferenceQuantum Physics and Logic 2019
Abbreviated titleQPL 2019
CountryUnited States
CityOrange
Period10/06/1914/06/19
Internet address

Keywords

  • quant-ph
  • math.CT

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