Strong Locality as a Tetrahedron: A Symmetry-Reduced Geometric Representation of the (3,3,2,2) Bell Scenario
Summarize this article with:
Quantum Physics arXiv:2605.03104 (quant-ph) [Submitted on 4 May 2026] Title:Strong Locality as a Tetrahedron: A Symmetry-Reduced Geometric Representation of the (3,3,2,2) Bell Scenario Authors:Marek Gazdzicki, Francesco Giacosa, Pawel Piesowicz View a PDF of the paper titled Strong Locality as a Tetrahedron: A Symmetry-Reduced Geometric Representation of the (3,3,2,2) Bell Scenario, by Marek Gazdzicki and Francesco Giacosa and Pawel Piesowicz View PDF HTML (experimental) Abstract:We present a geometric characterisation of strongly-local models in the bipartite Bell scenario with three measurement settings per site and binary outcomes, i.e.\ the (3,3,2,2) case. Restricting attention to indistinguishable sites, we introduce a three-dimensional mixed-moment space in which the mixed moments are calculated under off-diagonal measurement settings. In this reduced representation, the strongly-local region assumes the remarkably simple form of a regular tetrahedron - the 'pyramid'. We prove that only three independent linear inequalities are required to characterise this region. We call them the pyramid inequalities that separate strongly-local ($\mathcal{SL}$) models from their complement, non-strongly-local ($\mathcal{\overline{SL}}$) models. We also clarify the relation between the symmetry-reduced pyramid representation and the full (3,3,2,2) Bell polytope in the 36-dimensional conditional-probability space, which possesses 684 facet-defining inequalities. The reduction from 684 to three reflects normalisation, symmetry reduction, and projection to the mixed-moment space. In the pyramid representation, the hierarchy $\mathcal{SL} \subsetneq \mathcal{Q} \subsetneq \mathcal{NS}$ appears geometrically as a tetrahedron embedded in a somewhat larger curved body of quantum models, $\mathcal{Q}$, which in turn is embedded in a cube of no-signalling models, $\mathcal{NS}$. The qualitative and quantitative advantages of the pyramid representation over the standard CSHS representation for the (2,2,2,2) case are discussed. Comments: Subjects: Quantum Physics (quant-ph); High Energy Physics - Theory (hep-th) Cite as: arXiv:2605.03104 [quant-ph] (or arXiv:2605.03104v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2605.03104 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Marek Gazdzicki [view email] [v1] Mon, 4 May 2026 19:44:48 UTC (1,602 KB) Full-text links: Access Paper: View a PDF of the paper titled Strong Locality as a Tetrahedron: A Symmetry-Reduced Geometric Representation of the (3,3,2,2) Bell Scenario, by Marek Gazdzicki and Francesco Giacosa and Pawel PiesowiczView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-05 Change to browse by: hep-th 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?) 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?)