Three-uniform edge-ordered hypergraph quantum states: entanglement and its relation to hypergraph properties

Quantum Physics arXiv:2609.30399 (quant-ph) [Submitted on 24 Sep 2026] Title:Three-uniform edge-ordered hypergraph quantum states: entanglement and its relation to hypergraph properties Authors:N. A. Susulovska, Kh. P. Gnatenko View a PDF of the paper titled Three-uniform edge-ordered hypergraph quantum states: entanglement and its relation to hypergraph properties, by N. A. Susulovska and 1 other authors View PDF HTML (experimental) Abstract:The encoding of 3-uniform edge-ordered weighted hypergraphs into multiqubit quantum states is proposed. We derive an analytical expression for the geometric measure of entanglement of hypergraph quantum states and establish its relation to hypergraph properties. The results establish a direct connection between the local structure of hypergraphs, hyperedge weights, and the entanglement of the corresponding quantum states. For equally weighted hypergraphs, it is shown that the entanglement depends explicitly on the vertex degree. The dependence of entanglement on hypergraph parameters is studied analytically and using quantum computing. Hypergraph states associated with chain, star, regular lattice, and binary-tree hypergraphs are examined, and their entanglement is quantified using quantum computing. These results open up the possibility of studying hypergraph properties with quantum programming. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2609.30399 [quant-ph] (or arXiv:2609.30399v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2609.30399 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Nataliia Susulovska [view email] [v1] Thu, 24 Sep 2026 18:04:35 UTC (7,410 KB) Full-text links: Access Paper: View a PDF of the paper titled Three-uniform edge-ordered hypergraph quantum states: entanglement and its relation to hypergraph properties, by N. A. Susulovska and 1 other authorsView PDFHTML (experimental)TeX Source view license Current browse context: quant-ph new | recent | 2026-09 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?) 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?)