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A stabilizer $\mathrm{AME}(4,6)$ state does not exist

arXiv Quantum Physics
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⚡ Quantum Brief
Hyunho Cha mathematically proved that stabilizer absolutely maximally entangled (AME) states cannot exist for four six-dimensional qudits, resolving a key open question in quantum information theory. The research, published in March 2026, focuses on stabilizer states—a computationally efficient quantum state subclass—demonstrating their limitations in achieving maximal entanglement across all possible bipartitions. This non-existence result challenges prior assumptions about constructing high-dimensional AME states, which are critical for quantum error correction, holographic codes, and multi-party cryptography. The proof specifically targets the (4,6) configuration, where four parties share six-level quantum systems, a case previously considered plausible but now ruled out for stabilizer frameworks. The findings narrow the search for AME states, pushing researchers toward non-stabilizer methods or alternative entanglement structures to achieve similar quantum advantages.
A stabilizer $\mathrm{AME}(4,6)$ state does not exist

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Quantum Physics arXiv:2603.13442 (quant-ph) [Submitted on 13 Mar 2026] Title:A stabilizer $\mathrm{AME}(4,6)$ state does not exist Authors:Hyunho Cha View a PDF of the paper titled A stabilizer $\mathrm{AME}(4,6)$ state does not exist, by Hyunho Cha View PDF HTML (experimental) Abstract:We prove the non-existence of stabilizer absolutely maximally entangled states for systems of four six-dimensional qudits. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2603.13442 [quant-ph] (or arXiv:2603.13442v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2603.13442 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Hyunho Cha [view email] [v1] Fri, 13 Mar 2026 12:53:15 UTC (3 KB) Full-text links: Access Paper: View a PDF of the paper titled A stabilizer $\mathrm{AME}(4,6)$ state does not exist, by Hyunho ChaView 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?)

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Source: arXiv Quantum Physics