Two Roads to Classicality

TL;DR

This paper explores the conditions under which mixing and decoherence, two pathways to classicality in quantum theory, coincide, using category theory to unify and analyze these phenomena.

Contribution

It establishes a category-theoretic framework showing when mixing and decoherence lead to the same classical structures in quantum and other theories.

Findings

In quantum theory, both pathways produce C*-algebras and CP maps.

Counterexamples show the coincidence fails in relational and modal theories.

A new interpretation of decoherence as 'leaking information' is proposed.

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'.