Total and Partial Computation in Categorical Quantum Foundations

Kenta Cho
(Radboud University, Nijmegen)

This paper uncovers the fundamental relationship between total and partial computation in the form of an equivalence of certain categories. This equivalence involves on the one hand effectuses, which are categories for total computation, introduced by Jacobs for the study of quantum/effect logic. On the other hand, it involves what we call FinPACs with effects; they are finitely partially additive categories equipped with effect algebra structures, serving as categories for partial computation. It turns out that the Kleisli category of the lift monad (-)+1 on an effectus is always a FinPAC with effects, and this construction gives rise to the equivalence. Additionally, state-and-effect triangles over FinPACs with effects are presented.

In Chris Heunen, Peter Selinger and Jamie Vicary: Proceedings of the 12th International Workshop on Quantum Physics and Logic (QPL 2015), Oxford, U.K., July 15-17, 2015, Electronic Proceedings in Theoretical Computer Science 195, pp. 116–135.
Published: 4th November 2015.

ArXived at: http://dx.doi.org/10.4204/EPTCS.195.9 bibtex PDF
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