Universal Properties of Partial Quantum Maps

Pablo Andrés-Martínez, Chris Heunen, Robin Kaarsgaard

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Abstract

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.
OriginalsprogEngelsk
TitelProceedings 19th International Conference on Quantum Physics and Logic
Antal sider16
Vol/bind394
ForlagOpen Publishing Association
Publikationsdato16. nov. 2023
Sider192-207
StatusUdgivet - 16. nov. 2023
BegivenhedQuantum Physics and Logic Annual Conference - Wolfson College, London, Storbritannien
Varighed: 27. jun. 20221. jul. 2022

Konference

KonferenceQuantum Physics and Logic Annual Conference
LokationWolfson College
Land/OmrådeStorbritannien
ByLondon
Periode27/06/202201/07/2022
NavnElectronic Proceedings in Theoretical Computer Science
ISSN2075-2180

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