English

Order Unit Spaces and Probabilistic Models

Quantum Physics 2026-03-09 v1

Abstract

We exhibit a functor from the category OUS of order unit spaces and positive, unit-preserving mappings into the category \Prob\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.

Keywords

Cite

@article{arxiv.2603.05682,
  title  = {Order Unit Spaces and Probabilistic Models},
  author = {John Harding and Alex Wilce},
  journal= {arXiv preprint arXiv:2603.05682},
  year   = {2026}
}
R2 v1 2026-07-01T11:05:46.240Z