Mermin's Inequality
M = ⟨X₁X₂Y₃⟩+⟨X₁Y₂X₃⟩+⟨Y₁X₂X₃⟩−⟨Y₁Y₂Y₃⟩
Classical bound: M ≤ 2
Quantum (GHZ): M = 4
GHZ gives the maximum possible violation — even stronger than Bell's inequality. The correlations are instantaneous across any distance, but cannot be used for faster-than-light signaling.
Classical limit at 2.0 (50%)
Physics
GHZ (Greenberger-Horne-Zeilinger) state was proposed in 1989 as a "no-statistics" proof of nonlocality.
Unlike Bell tests, a single measurement outcome contradicts local hidden variables — no statistical aggregation needed.
If Q1=0, then Q2=Q3=0 with certainty.
If Q1=1, then Q2=Q3=1 with certainty.
Circuit: H on Q1, then CNOT(Q1→Q2), CNOT(Q1→Q3).