Bell Inequality — CHSH Test of Quantum Entanglement

Alice and Bob each choose a measurement angle. For an entangled singlet |ψ⁻⟩, quantum mechanics predicts E(a,b)=−cos(a−b). The CHSH inequality S=|E(a,b)−E(a,b′)+E(a′,b)+E(a′,b′)|≤2 is violated by QM up to 2√2≈2.828.

Measurement Angles (degrees)

Alice a 0° Alice a′ 90° Bob b 45° Bob b′ 135°

Experiment

Samples per run 1000 Model Quantum

Results

E(a,b) —

E(a,b′) —

E(a′,b) —

E(a′,b′) —

CHSH S —

Run experiment

Classical bound: S ≤ 2
Quantum maximum: S = 2√2 ≈ 2.828 (Tsirelson bound)
Singlet: E(θ) = −cos(θ)