{"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 states","topic_ref":"b07684c5fe91d012cf3f7701521f464b6170695b71db99db565aa3f747a6411c"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"e1a967ddc136d31a17c8d2e930931278405fcb1dad85e098eb7ab124332911b5","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"f533824e8b0d6f7ca13c683bdffd5dab10f2ad3f0596a2d1064b1355c3448c08","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"-HKJTkTM-3hgDjOOwrZiZ9nAdJZL1tVX9S3kOG1nf-NvdEInhS4TDqhCqCziZs0S-mHqym2iNVxzG9TOhANdBg"},"schema":"pubphys.envelope/1"},"record_hash":"e1a967ddc136d31a17c8d2e930931278405fcb1dad85e098eb7ab124332911b5","leaf_index":1987}