Consistency of Generalised Probabilistic Theories is Undecidable
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Quantum Physics arXiv:2603.07002 (quant-ph) [Submitted on 7 Mar 2026] Title:Consistency of Generalised Probabilistic Theories is Undecidable Authors:Serge Massar View a PDF of the paper titled Consistency of Generalised Probabilistic Theories is Undecidable, by Serge Massar View PDF Abstract:Generalised Probabilistic Theories (GPTs) provide a unifying framework encompassing classical theories, quantum theories, as well as hypothetical alternatives. We investigate the problem of extending a system with a finite set of transformations. We also investigate the problem of adding to a translation invariant set of systems a finite set of entangled states and effects, plus all their images by the translation symmetry. We show that determining whether such extensions are consistent with the axioms of GPTs is undecidable: they are computationally equivalent to the halting problem for Turing machines. The source of the undecidability is that these finite extensions generate infinitely many conditions which must be checked, because iterating transformations produces infinitely many new transformations, and similarly, entangled states and effects generate infinitely many new states via the analog of teleportation. Our results show that extending GPTs to include dynamics or entanglement encounters fundamental computability obstructions, which can only be circumvented by introducing additional physical or mathematical assumptions. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.07002 [quant-ph] (or arXiv:2603.07002v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.07002 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Serge Massar [view email] [v1] Sat, 7 Mar 2026 02:53:32 UTC (19 KB) Full-text links: Access Paper: View a PDF of the paper titled Consistency of Generalised Probabilistic Theories is Undecidable, by Serge MassarView PDFTeX Source view license Current browse context: quant-ph new | recent | 2026-03 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?)