Geometric characterization of non-Gaussian entanglement for finite stellar rank states

Quantum Physics arXiv:2511.02076 (quant-ph) [Submitted on 3 Nov 2025] Title:Geometric characterization of non-Gaussian entanglement for finite stellar rank states Authors:Carlos E. Lopetegui-Gonzalez, Massimo Frigerio, Mattia Walschaers View a PDF of the paper titled Geometric characterization of non-Gaussian entanglement for finite stellar rank states, by Carlos E. Lopetegui-Gonzalez and 1 other authors View PDF HTML (experimental) Abstract:We introduce a general framework for the analysis of non-Gaussian entanglement in bosonic states of finite stellar rank. The central result is the full characterization of their entanglement structure through the atomic decomposition of their stellar polynomial and its associated structural graph, whose connected components determine the mode-intrinsic entanglement content of the state and all partitions compatible with passive separability. An essential ingredient in this construction is the concept of essential variables, which identify the minimal number of effective modes involved in a core state, in direct correspondence with the symplectic rank. This reduction provides the foundation for decomposing stellar polynomials into atomic factors and for revealing the underlying entanglement structure. Building on this, we derive complete separability criteria for two-mode states, expressed through hyperplane decompositions of zero sets, and for stellar-rank-2 states across arbitrary number of modes. Applications to several example states illustrate how the method isolates genuinely non-Gaussian resources and quantifies preparation complexity. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2511.02076 [quant-ph] (or arXiv:2511.02076v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2511.02076 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Carlos E. Lopetegui Gonzalez [view email] [v1] Mon, 3 Nov 2025 21:28:49 UTC (296 KB) Full-text links: Access Paper: View a PDF of the paper titled Geometric characterization of non-Gaussian entanglement for finite stellar rank states, by Carlos E. Lopetegui-Gonzalez and 1 other authorsView 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?)