E91 Bell Test: Correlation Curve & CHSH Verification (2D)

The E91 protocol distributes a secret key from entangled photon pairs and certifies the channel's security with a live Bell-inequality violation instead of an assumption about the source. This 2D simulation makes that certification visible as data rather than as scenery: two polarizer dials show Alice's and Bob's analyzer angles for each emitted pair while a scrolling scatter chart accumulates the measured correlation E(Δ) = ⟨r_Ar_B⟩ across the full range of angle differences Δ and compares it, bin by bin, against the theoretical −cos(Δ) singlet-state curve. In parallel, Ekert's original three-angle measurement sets feed a running CHSH statistic S, and matching-basis rounds sift into a shared secret key. An adjustable intercept-resend eavesdropping attack lets you watch both signatures of a compromised channel appear together in real time: the correlation dots peel away from the theoretical curve, S drifts from the quantum maximum 2√2 ≈ 2.828 down through the classical bound of 2, and the sifted key's bit-error rate climbs.