CHSH Bell Inequality — Quantum vs Classical Correlations

S = |E(a,b) - E(a,b') + E(a',b) + E(a',b')| — classical ≤2, quantum ≤2√2 ≈ 2.828 (Tsirelson bound)

E(a,b) = -cos(a-b)
CHSH value:
S = 2.828
Classical bound: S ≤ 2
Tsirelson bound: S ≤ 2√2
Violated: YES ✓
Correlations:
E(a,b) = ?
E(a,b') = ?
E(a',b) = ?
E(a',b') = ?
Optimal angles:
a=0°, a'=45°, b=22.5°, b'=67.5°
Gives S=2√2 exactly