aiqbench analysis
This paper establishes a rigorous mathematical framework where general probabilistic theories admit canonical classical explanations, effectively bridging abstract quantum-like structures with standard non-local representations via functorial constructions. By demonstrating that locally-finite models possess sharp classical counterparts through specific categorical spans and pullbacks, the work advances foundational understanding of how complex probabilistic systems can be interpreted within a classical context without relying on traditional local realism assumptions.
Classical Explanations in (and of) General Probabilistic Theories
arXiv:2603.05627v2 Announce Type: replace Abstract: We introduce a notion of the ``explanation" of one (generalized) probabilistic model by another as particular kind of span in the category $\Prob$ of probabilistic models and morphisms. We show that explanations compose under a standard pullback construction (notwithstanding that $\Prob$ does not support arbitrary pullbacks). We then show that every locally-finite probabilistic model has a canonical, sharp classical explanation. The construction is functorial, so every locally-finite probabilistic theory has a canonical, sharp classical (though of course, usually non-local) representation.
Abstract:We introduce a notion of the ``explanation" of one (generalized) probabilistic model by another as particular kind of span in the category $\Prob$ of probabilistic models and morphisms. We show that explanations compose under a standard pullback construction (notwithstanding that $\Prob$ does not support arbitrary pullbacks). We then show that every locally-finite probabilistic model has a canonical, sharp classical explanation. The construction is functorial, so every locally-finite probabilistic theory has a canonical, sharp classical (though of course, usually non-local) representation.
Quantum Physics (quant-ph); Logic in Computer Science (cs.LO)
arXiv:2603.05627 [quant-ph]
(or arXiv:2603.05627v2 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2603.05627 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 177 words
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