Universal Properties of Partial Quantum Maps
Quantum Physics
2023-11-16 v2 Logic in Computer Science
Category Theory
Operator Algebras
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.
Cite
@article{arxiv.2206.04814,
title = {Universal Properties of Partial Quantum Maps},
author = {Pablo Andrés-MartíÂ-nez and Chris Heunen and Robin Kaarsgaard},
journal= {arXiv preprint arXiv:2206.04814},
year = {2023}
}
Comments
In Proceedings QPL 2022, arXiv:2311.08375