2024/03/28 by Cihan Okay, Okay, Cihan, Walker H. Stern +1 · 1 citation
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Mathematics and Applications #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2403.19808
We introduce a theory of twisted simplicial distributions on simplicial principal bundles, which allow us to capture Bell's non-locality, and the more general notion of quantum contextuality. We leverage the classical theory of simplicial principal bundles, as well as structures on categories of such bundles, to provide powerful computational tools for analyzing twisted distributions in terms of both direct constructions in simplicial sets and techniques from homological algebra. We use these techniques to analyze our key examples: quantum distributions and operator-theoretic polytopes used in the classical simulation of quantum computation.