{"paper":{"title":"Better local hidden variable models for two-qubit Werner states and an upper bound on the Grothendieck constant $K_G(3)$","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math-ph","math.FA","math.MP"],"primary_cat":"quant-ph","authors_text":"Flavien Hirsch, Marco T\\'ulio Quintino, Miguel Navascu\\'es, Nicolas Brunner, Tam\\'as V\\'ertesi","submitted_at":"2016-09-20T11:42:24Z","abstract_excerpt":"We consider the problem of reproducing the correlations obtained by arbitrary local projective measurements on the two-qubit Werner state $\\rho = v |\\psi_- > <\\psi_- | + (1- v ) \\frac{1}{4}$ via a local hidden variable (LHV) model, where $|\\psi_- >$ denotes the singlet state. We show analytically that these correlations are local for $ v = 999\\times689\\times{10^{-6}}$ $\\cos^4(\\pi/50) \\simeq 0.6829$. In turn, as this problem is closely related to a purely mathematical one formulated by Grothendieck, our result implies a new bound on the Grothendieck constant $K_G(3) \\leq 1/v \\simeq 1.4644$. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.06114","kind":"arxiv","version":4},"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"}