Sub-Planck structure quantification in non-Gaussian probability densities
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Quantum Physics arXiv:2601.05898 (quant-ph) [Submitted on 9 Jan 2026] Title:Sub-Planck structure quantification in non-Gaussian probability densities Authors:Darren W. Moore, Vojtěch Švarc, Kratveer Singh, Artem Kovalenko, Minh Tuan Pham, Ondřej Číp, Lukáš Slodička, Radim Filip View a PDF of the paper titled Sub-Planck structure quantification in non-Gaussian probability densities, by Darren W. Moore and 7 other authors View PDF HTML (experimental) Abstract:Sub-Planck structures in non-Gaussian probability densities of phase space variables are pervasive in bosonic quantum systems. They are almost universally present if the bosonic system evolves via nonlinear dynamics or nonlinear measurements. So far, identification and comparison of such structures remains qualitative. Here we provide a universally applicable and experimentally friendly method to identify, quantify and compare sub-Planck structures from directly measurable or estimated probability densities of single phase space variables. We demonstrate the efficacy of this method on experimental high order Fock states of a single-atom mechanical oscillator, showing provably finer sub-Planck structures as the Fock occupation increases despite the accompanying uncertainty increase in the phonon, position, and momentum bases. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2601.05898 [quant-ph] (or arXiv:2601.05898v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2601.05898 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Darren Moore [view email] [v1] Fri, 9 Jan 2026 16:17:04 UTC (829 KB) Full-text links: Access Paper: View a PDF of the paper titled Sub-Planck structure quantification in non-Gaussian probability densities, by Darren W. Moore and 7 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?)