Universal Properties of Partial Quantum Maps

Pablo Andrés-Martínez, Chris Heunen, Robin Kaarsgaard

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We provide a universal construction of the category of finite-dimensional C*-algebras and completely positive trace-nonincreasing maps from the rig category of finite-dimensional Hilbert spaces and unitaries. This construction, which can be applied to any dagger rig category, is described in three steps, each associated with their own universal property, and draws on results from dilation theory in finite dimension. In this way, we explicitly construct the category that captures hybrid quantum/classical computation with possible nontermination from the category of its reversible foundations. We discuss how this construction can be used in the design and semantics of quantum programming languages.
Original languageEnglish
Title of host publicationProceedings 19th International Conference on Quantum Physics and Logic
Number of pages16
PublisherOpen Publishing Association
Publication date16. Nov 2023
Publication statusPublished - 16. Nov 2023
EventQuantum Physics and Logic Annual Conference - Wolfson College, London, United Kingdom
Duration: 27. Jun 20221. Jul 2022


ConferenceQuantum Physics and Logic Annual Conference
LocationWolfson College
Country/TerritoryUnited Kingdom
SeriesElectronic Proceedings in Theoretical Computer Science


  • quant-ph
  • cs.LO
  • math.CT
  • math.OA


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