Extremal Magic States from Symmetric Lattices

[2506.11725] Extremal Magic States from Symmetric Lattices Skip to main content Search Submit Donate Log in Quantum Physics arXiv:2506.11725 (quant-ph) [Submitted on 13 Jun 2025 ( v1 ), last revised 28 Aug 2026 (this version, v2)] Title: Extremal Magic States from Symmetric Lattices Authors: Misaki Ohta , Kazuki Sakurai View PDF HTML (experimental) Abstract: Magic, a key quantum resource beyond entanglement, remains poorly understood in terms of its structure and classification. In this paper, we demonstrate a striking connection between high-dimensional symmetric lattices and quantum magic states. By mapping vectors from the $E_8, B W_{16}$, and $E_6$ lattices into Hilbert space, we construct and classify stabiliser and maximal magic states for two-qubit, three-qubit and one-qutrit systems. In particular, this geometric approach gives closed-form lattice representatives of maximal magic states and motivates a conjecture for the number of three-qubit maximal states. In the three-qubit case, we further classify the extremal magic states according to their entanglement structure. We also show that the 45 one-qutrit maximal magic states selected by the second shell of $E_6$ split into two Clifford orbits. Our findings suggest that deep algebraic and geometric symmetries underlie the structure of extremal magic states. Comments: 28 pages, 6 figures, 4 tables Subjects: Quantum Physics (quant-ph) ; High Energy Physics - Phenomenology (hep-ph); High Energy Physics - Theory (hep-th); Mathematical Physics (math-ph) Cite as: arXiv:2506.11725 [quant-ph] (or arXiv:2506.11725v2 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2506.11725 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Misaki Ohta [ view email ] [v1] Fri, 13 Jun 2025 12:39:40 UTC (1,901 KB) [v2] Fri, 28 Aug 2026 08:43:43 UTC (1,900 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: quant-ph < prev | next > new | recent | 2025-06 Change to browse by: hep-ph hep-th math math-ph math.MP References & Citations INSPIRE HEP SciX 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 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? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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