@inproceedings{bfa3a9b45c4246f4bfac4bbf2298b5eb,

title = "Universal Properties of Partial Quantum Maps",

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. ",

keywords = "quant-ph, cs.LO, math.CT, math.OA",

author = "Pablo Andr{\'e}s-Mart{\'i}nez and Chris Heunen and Robin Kaarsgaard",

year = "2023",

month = nov,

day = "16",

language = "English",

volume = "394",

series = "Electronic Proceedings in Theoretical Computer Science",

publisher = "Open Publishing Association",

pages = "192--207",

booktitle = "Proceedings 19th International Conference on Quantum Physics and Logic",

note = "Quantum Physics and Logic Annual Conference, QPL 2022 ; Conference date: 27-06-2022 Through 01-07-2022",

}