Universal Properties of Partial Quantum Maps

Pablo Andres Martinez, Chris Heunen, Robin Kaarsgaard

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

Abstract / Description of output

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 of the 19th International Conference on Quantum Physics and Logic
Number of pages17
Publication statusAccepted/In press - 1 Jun 2022
EventThe 19th International Conference on Quantum Physics and Logic 2022 - Oxford, United Kingdom
Duration: 27 Jun 20221 Jul 2022
Conference number: 19


ConferenceThe 19th International Conference on Quantum Physics and Logic 2022
Abbreviated titleQPL 2022
Country/TerritoryUnited Kingdom
Internet address


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