Establishes a complete axiomatization for probabilistic Boolean circuits via Markov kernel semantics, using intermediate completeness theorems for partial Boolean circuits and probabilistic Boolean tapes in rig categories.
Two Roads to Classicality
2 Pith papers cite this work. Polarity classification is still indexing.
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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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cs.LO 2verdicts
UNVERDICTED 2representative citing papers
Kleene-Cartesian rig categories equip tape diagrams to handle imperative programs and program logic.
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Completeness for Probabilistic Boolean Tapes
Establishes a complete axiomatization for probabilistic Boolean circuits via Markov kernel semantics, using intermediate completeness theorems for partial Boolean circuits and probabilistic Boolean tapes in rig categories.
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A Diagrammatic Basis for Computer Programming
Kleene-Cartesian rig categories equip tape diagrams to handle imperative programs and program logic.