Properties and Applications of Partially Deterministic Polytopes

Quantum Physics arXiv:2510.25127 (quant-ph) [Submitted on 29 Oct 2025] Title:Properties and Applications of Partially Deterministic Polytopes Authors:Marwan Haddara, Howard M. Wiseman, Eric G. Cavalcanti View a PDF of the paper titled Properties and Applications of Partially Deterministic Polytopes, by Marwan Haddara and Howard M. Wiseman and Eric G. Cavalcanti View PDF Abstract:The assumption of a deterministic local hidden variable model constrains the experimentally accessible statistics in a Bell experiment to be contained in the Bell-local polytope. But what if the outputs for only a subset of the measurements at each site are predetermined by the model? In this work, we thoroughly explore this concept of `partial determinism', allowing for arbitrary numbers of parties, inputs and outputs per site. The resulting objects form new classes of convex polytopes which recover the Bell and the no-signalling polytopes as special cases. Nontrivial equivalence classes of partially deterministic models arise, which we classify completely. In particular, the Bell polytope for any scenario can be expressed in multiple different ways in terms of local partially deterministic models. This allows us to generalise Fine's theorem, recovering the original formulation as a special case, but finding new constraints otherwise. We discuss scenarios with different physical motivations, which do not require the causal structure of the Bell scenario, and where classes of partially deterministic polytopes are relevant. Our example applications include device-independent quantum state inseparability witnesses, classes of broadcast-local polytopes, and Local Friendliness scenarios in quantum foundations. We also point out instances in previous literature where classes of related objects have been studied. In the case of correlations compatible with the Local Friendliness assumptions, we find a one-to-one correspondence between partially deterministic polytopes and sequential extended Wigner's friend scenarios so that every partially deterministic polytope has physical relevance. We discuss how the framework captures a broad class of non-classicality notions, and identify an even broader notion of `composable sets', of which partially deterministic polytopes are special cases. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2510.25127 [quant-ph] (or arXiv:2510.25127v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2510.25127 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Marwan Haddara [view email] [v1] Wed, 29 Oct 2025 03:09:11 UTC (799 KB) Full-text links: Access Paper: View a PDF of the paper titled Properties and Applications of Partially Deterministic Polytopes, by Marwan Haddara and Howard M. Wiseman and Eric G. CavalcantiView PDFTeX Source view license Current browse context: quant-ph new | recent | 2025-10 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)