{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-concrete-model-for-the-quantum-permutation","title":"A Concrete Model for the Quantum Permutation Group on 4 Points","arxiv_id":"2304.09124","date":"2023-04-18","proceeding":null,"authors":["Nicolas Faroß","Moritz Weber"],"abstract":"In 2019, Jung-Weber gave an example of a concrete magic unitary $M$, which defines a $C^*$-algebraic model of the quantum permutation group $S_4^+$. We show with the help of a computer that there exist no polynomials up to degree $50$ separating the entries of $M$ from the generators of $C(S_4^+)$. This indicates that the magic unitary $M$ might already define a faithful model of $S_4^+$.","url_abs":"https://arxiv.org/abs/2304.09124v1","url_pdf":"https://arxiv.org/pdf/2304.09124v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"a-concrete-model-for-the-quantum-permutation","repo_url":"https://github.com/nfaross/model-s4plus","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}