2015/06/30 by Chris Heunen, Sean Tull
Mathematics · Computer Science · Physics and Astronomy · #math.CT #cs.LO #quant-ph
paper · pdf · doi:10.4204/eptcs.195.18
published as EPTCS 195, 2015, pp. 247-261 · In Proceedings QPL 2015, arXiv:1511.01181
arxiv created 2015/11/05 · arxiv updated 2015/11/06
Categories of relations over a regular category form a family of models of quantum theory. Using regular logic, many properties of relations over sets lift to these models, including the correspondence between Frobenius structures and internal groupoids. Over compact Hausdorff spaces, this lifting gives continuous symmetric encryption. Over a regular Mal'cev category, this correspondence gives a characterization of categories of completely positive maps, enabling the formulation of quantum features. These models are closer to Hilbert spaces than relations over sets in several respects: Heisenberg uncertainty, impossibility of broadcasting, and behavedness of rank one morphisms.