On Non-Existence of Stabilizer Absolutely Maximally Entangled States in Even Local Dimensions

Quantum Physics [Submitted on 18 Mar 2026] On Non-Existence of Stabilizer Absolutely Maximally Entangled States in Even Local Dimensions Jakub Wójcik, Owidiusz Makuta, Wojciech Bruzda, Remigiusz Augusiak 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 Submission history From: Wojciech Bruzda [view email] [v1] Wed, 18 Mar 2026 18:41:57 UTC (11 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation 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 Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)