Bell/CHSH Inequalities: Unified Rules and Ballistic-Electron Testbeds — E8 Intelligence Research

FINDING: Bell/CHSH inequalities define the boundary between classical local-hidden-variable theories and quantum correlations; recent work (Buscemi) reformulates them as a unified family of "rules" covering entanglement and nonlocality, and new physical platforms (ballistic electrons in semiconductor quantum wires) are proposed as testbeds. MATH: - CHSH inequality (classical bound): |E(a,b) − E(a,b′) + E(a′,b) + E(a′,b′)| ≤ 2 - Quantum (Tsirelson) bound: same expression ≤ 2√2 ≈ 2.828 - Quantum/classical ratio: 2√2 / 2 = √2 ≈ 1.4142 - Maximal violation angle for singlet state: correlations E(a,b) = −a·b; optimal settings at 45° increments give S = 2√2 - General Bell functional: S = Σ_{x,y} w_{xy} P(a,b|x,y); local polytope bounded by facet inequalities; quantum set Q strictly contains local polytope L, strictly contained in no-signaling set NS - Buscemi's unification: inequalities expressed via conditional min-/max-entropy constraints — "new rules" generalize CHSH to entropy-based Bell Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com