Two roads to classicality

Abstract

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 provide a new interpretation for our category-Theoretic generalisation of decoherence in terms of 'leaking information'. andcopy; B. Coecke, J. Selby andamp; S. Tull This work is licensed under the Creative Commons Attribution License.