Two Roads to Classicality

@inproceedings{Coecke2017TwoRT,
  title={Two Roads to Classicality},
  author={Bob Coecke and John H. Selby and Sean Tull},
  year={2017}
}
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… 

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