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Purity through Factorisation

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arxiv 1705.07652 v2 pith:QRAJXFDF submitted 2017-05-22 quant-ph cs.LO

Oscar Cunningham (University of Oxford) , Chris Heunen (University of Edinburgh) This is my paper · ORCID
classification quant-phcs.LO
keywords pureconstructionfactorisationprocessesarisescategoricalcategoriesclassical
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We give a construction that identifies the collection of pure processes (i.e. those which are deterministic, or without randomness) within a theory containing both pure and mixed processes. Working in the framework of symmetric monoidal categories, we define a pure subcategory. This definition arises elegantly from the categorical notion of a weak factorisation system. Our construction gives the expected result in several examples, both quantum and classical.

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  1. A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics

    math.ST 2019-08 conditional novelty 7.0 of 10

    Markov categories provide a synthetic, axiom-based framework in which conditional independence, sufficiency, completeness, and classical theorems such as Basu and Bahadur hold uniformly across many probability theories.

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