{"paper":{"title":"Approximate quantum 3-colorings of graphs and the quantum Max 3-Cut problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"quant-ph","authors_text":"Samuel J. Harris","submitted_at":"2024-12-27T02:05:37Z","abstract_excerpt":"We prove that, to each synchronous non-local game $\\mathcal{G}=(I,O,\\lambda)$ with $|I|=n$ and $|O|=m \\geq 3$, there is an associated graph $G_{\\lambda}$ for which approximate winning strategies for the game $\\mathcal{G}$ and the $3$-coloring game for $G_{\\lambda}$ are preserved. That is, using a similar graph to previous work of the author (Ann. Henri Poincar\\'{e}, 2024), any synchronous strategy for $\\text{Hom}(G_{\\lambda},K_3)$ that wins the game with probability $1-\\varepsilon$ with respect to the uniform probability distribution on the edges, yields a strategy in the same model that wins "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2412.19405","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2412.19405/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}