Against probability: A quantum state is more than a list of probability distributions
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Quantum Physics arXiv:2601.18872 (quant-ph) [Submitted on 26 Jan 2026] Title:Against probability: A quantum state is more than a list of probability distributions Authors:Ladina Hausmann, Renato Renner View a PDF of the paper titled Against probability: A quantum state is more than a list of probability distributions, by Ladina Hausmann and 1 other authors View PDF HTML (experimental) Abstract:The state $\rho$ of a quantum system can be represented by a vector $\mathbf{P}_{\mathcal{M}}(\rho)$ of outcome probabilities for a set of measurements $\mathcal{M}$. Such representations appear throughout physics, for example, in quantum field theory via correlation functions and in quantum foundations within generalized probabilistic frameworks. In this work, we identify an unavoidable tension: to enable operationally meaningful statements, the map ${\rho \mapsto \mathbf{P}_{\mathcal{M}}(\rho)}$ must be topologically robust $\unicode{x2013}$ preserving the notion of closeness between states. Yet, a probability representation that is topologically robust cannot simultaneously retain other essential structure, such as the subsystem structure. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.18872 [quant-ph] (or arXiv:2601.18872v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.18872 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Ladina Hausmann [view email] [v1] Mon, 26 Jan 2026 19:00:01 UTC (49 KB) Full-text links: Access Paper: View a PDF of the paper titled Against probability: A quantum state is more than a list of probability distributions, by Ladina Hausmann and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-01 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?)