Bell Test — CHSH Inequality & Quantum Violation

Entangled photon pairs: quantum correlations E(θ) = −cos(2θ) violate |S|≤2 (classical bound)

Measurement Angles

CHSH Parameter

S = 2.828
Classical max |S| = 2
Quantum max |S| = 2√2 ≈ 2.828

Theory

Singlet state |ψ⁻⟩: E(a,b) = −cos(2(a−b))

CHSH: S = E(a,b)−E(a,b')+E(a',b)+E(a',b')

Local hidden variable: |S| ≤ 2
Quantum mechanics: |S| ≤ 2√2

Optimal angles: a=0°, a'=45°,
b=22.5°, b'=67.5° → S=2√2

Loopholes: detection, locality
Closed by Hensen et al 2015