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.
A generalized no-broadcasting theorem
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abstract
We prove a generalized version of the no-broadcasting theorem, applicable to essentially \emph{any} nonclassical finite-dimensional probabilistic model satisfying a no-signaling criterion, including ones with ``super-quantum'' correlations. A strengthened version of the quantum no-broadcasting theorem follows, and its proof is significantly simpler than existing proofs of the no-broadcasting theorem.
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math.ST 1years
2019 1verdicts
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A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics
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.