{"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/violation-of-the-finner-inequality-in-the","title":"Violation of the Finner inequality in the four-output triangle network","arxiv_id":"2306.05922","date":"2023-06-09","proceeding":null,"authors":["Antoine Girardin","Nicolas Gisin"],"abstract":"Network nonlocality allows one to demonstrate nonclassicality in networks with fixed joint measurements, that is without random measurement settings. The simplest network in a loop, the triangle, with 4 outputs per party is especially intriguing. The \"elegant distribution\" [N. Gisin, Entropy 21, 325 (2019)] still resists analytic proofs, despite its many symmetries. In particular, this distribution is invariant under any output permutation. The Finner inequality, which holds for all local and quantum distributions, has been conjectured to be also valid for all no-signalling distributions with independent sources (NSI distributions). Here we provide evidence that this conjecture is false by constructing a 4-output network box that violate the Finner inequality and prove that it satisfies all NSI inflations up to the enneagon. As a first step toward the proof of the nonlocality of the elegant distribution, we prove the nonlocality of the distributions that saturates the Finner inequality by using geometrical arguments.","url_abs":"https://arxiv.org/abs/2306.05922v2","url_pdf":"https://arxiv.org/pdf/2306.05922v2.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":"violation-of-the-finner-inequality-in-the","repo_url":"https://github.com/Antoine0Girardin/Inflation-OPI-4-triangle","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}