Pictures of complete positivity in arbitrary dimension
Bob Coecke, Chris Heunen (University of Oxford)
TL;DR
This paper extends the CP-construction to arbitrary dimensions in categorical quantum mechanics and provides axioms characterizing categories obtained through this process.
Contribution
It generalizes the CP-construction beyond finite dimensions and offers axioms to identify categories derived from this construction.
Findings
Generalization of CP-construction to arbitrary dimension
Axiomatization of categories resulting from the CP-construction
Framework for categorical quantum mechanics in higher dimensions
Abstract
Two fundamental contributions to categorical quantum mechanics are presented. First, we generalize the CP-construction, that turns any dagger compact category into one with completely positive maps, to arbitrary dimension. Second, we axiomatize when a given category is the result of this construction.
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