QM Research Seminar: Universal Properties of Partial Quantum Maps

Speaker: Robin Kaarsgaard Sales (University of Southern Denmark)

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.


This talk is based on joint work with Pablo Andrés-Martínez
(Quantinuum) and Chris Heunen (University of Edinburgh).