Correlation Self-Testing of Quantum Theory against Generalised Probabilistic Theories with Restricted Relabelling Symmetry

Quantum Physics arXiv:2511.02914 (quant-ph) [Submitted on 4 Nov 2025] Title:Correlation Self-Testing of Quantum Theory against Generalised Probabilistic Theories with Restricted Relabelling Symmetry Authors:Kuntal Sengupta, Mirjam Weilenmann, Roger Colbeck View a PDF of the paper titled Correlation Self-Testing of Quantum Theory against Generalised Probabilistic Theories with Restricted Relabelling Symmetry, by Kuntal Sengupta and Mirjam Weilenmann and Roger Colbeck View PDF HTML (experimental) Abstract:Correlation self-testing of quantum theory involves identifying a task or set of tasks whose optimal performance can be achieved only by theories that can realise the same set of correlations as quantum theory in every causal structure. Following this approach, previous work has ruled out various classes of generalised probabilistic theories whose joint state spaces have a certain regularity in the sense of a (discrete) rotation symmetry of the bipartite state spaces. Here we consider theories whose bipartite state spaces lack this regularity. We form them by taking the convex hull of all the local states and a finite number of non-local states. We show that a criterion of compositional consistency is needed in such theories: for a measurement effect to be valid, there must exist at least one measurement that it is part of. This goes beyond previous consistency criteria and corresponds to a strengthening of the no-restriction hypothesis. We show that quantum theory outperforms these theories in a task called the adaptive CHSH game, which shows that they can be ruled out experimentally. We further show a connection between compositional consistency and Tsirelson's bound. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2511.02914 [quant-ph] (or arXiv:2511.02914v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2511.02914 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Kuntal Sengupta [view email] [v1] Tue, 4 Nov 2025 19:00:19 UTC (152 KB) Full-text links: Access Paper: View a PDF of the paper titled Correlation Self-Testing of Quantum Theory against Generalised Probabilistic Theories with Restricted Relabelling Symmetry, by Kuntal Sengupta and Mirjam Weilenmann and Roger ColbeckView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2025-11 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?)