Two Roads to Classicality

Bob Coecke, John Selby, Sean Tull
2018 Electronic Proceedings in Theoretical Computer Science  
Mixing and decoherence are both manifestations of classicality within quantum theory, each of which admit a very general category-theoretic construction. We show under which conditions these two 'roads to classicality' coincide. This is indeed the case for (finite-dimensional) quantum theory, where each construction yields the category of C*-algebras and completely positive maps. We present counterexamples where the property fails which includes relational and modal theories. Finally, we
more » ... Finally, we provide a new interpretation for our category-theoretic generalisation of decoherence in terms of 'leaking information'.
doi:10.4204/eptcs.266.7 fatcat:5c6yhnpf5vc6fck3pq7unnvo4y