Quantum correlations exceed the classical bound S ≤ 2 (quantum max: 2√2 ≈ 2.828)
Alice & Bob Measurement Angles
E(a,b) = —
E(a,b') = —
E(a',b) = —
E(a',b') = —
S = —
About: Bell's theorem (1964) proves no local hidden variable theory can reproduce all quantum predictions. The CHSH inequality (Clauser-Horne-Shimony-Holt 1969) states that for any classical (local realistic) theory, |S| = |E(a,b) − E(a,b') + E(a',b) + E(a',b')| ≤ 2. For a maximally entangled singlet state, quantum mechanics predicts E(θ₁,θ₂) = −cos(θ₁−θ₂), and the optimal angle choice (0°, 45°, 22.5°, 67.5°) gives S = 2√2 ≈ 2.828 — violating the classical bound. Aspect et al. (1982) and many subsequent loophole-free experiments confirm quantum violation, ruling out local realism.