Paper
Order Unit Spaces and Probabilistic Models
Authors
John Harding, Alex Wilce
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.
Metadata
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Raw Data (Debug)
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"raw_xml": "<entry>\n <id>http://arxiv.org/abs/2603.05682v1</id>\n <title>Order Unit Spaces and Probabilistic Models</title>\n <updated>2026-03-05T21:16:05Z</updated>\n <link href='https://arxiv.org/abs/2603.05682v1' rel='alternate' type='text/html'/>\n <link href='https://arxiv.org/pdf/2603.05682v1' rel='related' title='pdf' type='application/pdf'/>\n <summary>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.</summary>\n <category scheme='http://arxiv.org/schemas/atom' term='quant-ph'/>\n <published>2026-03-05T21:16:05Z</published>\n <arxiv:primary_category term='quant-ph'/>\n <author>\n <name>John Harding</name>\n </author>\n <author>\n <name>Alex Wilce</name>\n </author>\n </entry>"
}