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Entanglement Theory Quantum Correlations Quantum Simulation

Order Unit Spaces and Probabilistic Models

arXiv
Authors: John Harding, Alex Wilce

Year

2026

Paper ID

28734

Status

Preprint

Abstract Read

~2 min

Abstract Words

96

Citations

N/A

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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  • 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...

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2603.05682 [2] arXiv https://arxiv.org/abs/2603.05682 [3] Publisher https://arxiv.org/abs/2603.05682

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