{"paper":{"title":"Complexity lower bounds for computing the approximately-commuting operator value of non-local games to high precision","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Matthew Coudron, William Slofstra","submitted_at":"2019-05-28T06:46:27Z","abstract_excerpt":"We study the problem of approximating the commuting-operator value of a two-player non-local game. It is well-known that it is $\\mathrm{NP}$-complete to decide whether the classical value of a non-local game is 1 or $1- \\epsilon$. Furthermore, as long as $\\epsilon$ is small enough, this result does not depend on the gap $\\epsilon$. In contrast, a recent result of Fitzsimons, Ji, Vidick, and Yuen shows that the complexity of computing the quantum value grows without bound as the gap $\\epsilon$ decreases. In this paper, we show that this also holds for the commuting-operator value of a game. Spe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.11635","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":""},"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"}