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arXiv · 1701.07400

Two Roads to Classicality

Bob Coecke·John Selby·Sean Tull
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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'.

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Bob Coecke, John Selby, Sean Tull. 2017-01-25. Two Roads to Classicality. https://doi.org/10.4204/eptcs.266.7

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