Order Unit Spaces and Probabilistic Models

John Harding; Alex Wilce

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arXiv · 2603.05682

Order Unit Spaces and Probabilistic Models

John Harding·Alex Wilce

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Abstract

We exhibit a functor from the category OUS of order unit spaces and positive, unit-preserving mappings into the category $\Prob$ of probabilistic models (test spaces with designated state spaces) and morphisms thereof. Restricted to any subcategory of OUS monoidal with respect to a positive, normalized, bilinear composition rule, our functor is also monoidal. This shows that the convex-operational approach to physical theories can be subsumed by the test-space approach, without resort to ``generalized test spaces''. A second construction, equipping a probabilistic model with tests representing ``weighted coins'', also sheds light on the nature of unsharp observables.

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John Harding, Alex Wilce. 2026-03-05. Order Unit Spaces and Probabilistic Models. https://arxiv.org/abs/2603.05682

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