{"paper":{"title":"No Finite NPA Level Characterizes the Complete Quantum Set in the Simplest Bell Scenario","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Anubhav Chaturvedi","submitted_at":"2026-07-16T04:52:11Z","abstract_excerpt":"The Navascu\\'es--Pironio--Ac\\'in (NPA) hierarchy gives the standard semidefinite outer approximations to quantum behaviors. Whether \\emph{any} finite level can already equal the quantum set has remained open even in the bipartite scenario with two binary measurements per party. We demonstrate that \\emph{no finite level} is exact. For the symmetric doubly tilted CHSH functional $h_\\alpha=A_0B_0+A_0B_1+A_1B_0-A_1B_1+\\alpha(A_0+B_0)$, set $T=1-\\alpha$. Its quantum maximum satisfies $[\\omega_{\\rm Q}(1-T)-(4-2T)]/T^3\\to4/3$, whereas every fixed NPA level satisfies $[\\omega_L(1-T)-\\omega_{\\rm Q}(1-T"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.14569","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/2607.14569/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"}