{"schema":"pubphys.bundle/1","record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"4d68a78f950c21580ce509a1c042bb32c2a0a5b2c967752d7e49e13becf964cd","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"1a5f5db4eebf944bd1a4e4fa15fa1787fae74b92e4fcd67ee6609806787b4957","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"value","assisted_by":[],"external_id":"qi.contextuality-nonlocality.werner-locality-threshold","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"A Werner state mixes a perfectly entangled pair with random noise. Below some noise level all projective-measurement results can be reproduced by classical hidden variables, and that exact level is unknown.","posed_since":"2006","precise":"For $\\rho_W(v) = v \\left|\\psi-\\right\\rangle\\left\\langle\\psi-\\right| + (1 - v) I/4$ ($I = 4x4$ identity matrix) with local projective measurements, the critical visibility above which some Bell inequality is violated is $v_c = 1/K_G(3)$, where $K_G(3)$ is the order-3 real Grothendieck constant. Current bounds $1.43670 \\le K_G(3) \\le 1.4546$ give $0.6875 \\le v_c \\le 0.69604$. Determine $v_c$.","problem_ref":null,"references":"","settled_by":"Matching local-model and Bell-inequality constructions fixing $v_{c}$ to all digits, or a closed form for $K_{G}(3)$.","status_note":"Lower bound $K_{G}(3) \\ge 1.43670$ (Designolle, Vertesi, Pokutta, PRA 2026, arXiv:2409.03739) and upper bound $K_{G}(3) \\le 1.4546$ from Frank-Wolfe local models (Designolle et al., 2023) give $0.6875 \\le v_{c} \\le 0.69604$.","title":"Exact nonlocality threshold of two-qubit Werner 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