Bell states are maximally entangled 2-qubit states. For |Φ⁺⟩, measuring Alice in basis a⃗ and Bob in b⃗:
⟨σ_A⊗σ_B⟩ = −a⃗·b⃗ (perfect anti-correlation for opposite bases). CHSH inequality:
|S| = |E(a,b) − E(a,b') + E(a',b) + E(a',b')| ≤ 2 (classical). Quantum max: 2√2 ≈ 2.828 (Tsirelson bound).
Violation proves no local hidden variable theory can explain the correlations.