On Non-Existence of Stabilizer Absolutely Maximally Entangled States in Even Local Dimensions
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Quantum Physics arXiv:2603.18193 (quant-ph) [Submitted on 18 Mar 2026] Title:On Non-Existence of Stabilizer Absolutely Maximally Entangled States in Even Local Dimensions Authors:Jakub Wójcik, Owidiusz Makuta, Wojciech Bruzda, Remigiusz Augusiak View a PDF of the paper titled On Non-Existence of Stabilizer Absolutely Maximally Entangled States in Even Local Dimensions, by Jakub W\'ojcik and 3 other authors View PDF HTML (experimental) Abstract:We demonstrate that absolutely maximally entangled (AME) states consisting of $N=4k$ qudits with $k\in\mathbb{N}_+$, each of even local dimension, cannot be realized as graph states. This result imposes strong constraints on AME states in composite local dimensions and characterizes the limitations of graph-state constructions for highly entangled multipartite quantum systems. In particular, this study provides an independent solution of the recently discussed case of the AME state of four quhexes and clarifies its characterization within the stabilizer formalism, complementing the results of Cha [arXiv:2603.13442]. Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.18193 [quant-ph] (or arXiv:2603.18193v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.18193 Focus to learn more arXiv-issued DOI via DataCite (pending registration) Submission history From: Wojciech Bruzda [view email] [v1] Wed, 18 Mar 2026 18:41:57 UTC (11 KB) Full-text links: Access Paper: View a PDF of the paper titled On Non-Existence of Stabilizer Absolutely Maximally Entangled States in Even Local Dimensions, by Jakub W\'ojcik and 3 other authorsView PDFHTML (experimental)TeX 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?)