Universal Properties of Partial Quantum Maps
- URL: http://arxiv.org/abs/2206.04814v2
- Date: Wed, 15 Nov 2023 18:57:25 GMT
- Title: Universal Properties of Partial Quantum Maps
- Authors: Pablo Andr\'es-Mart\'i\^A-nez (Quantinuum), Chris Heunen (University
of Edinburgh), Robin Kaarsgaard (University of Southern Denmark)
- Abstract summary: 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.
We discuss how this construction can be used in the design and semantics of quantum programming languages.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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