E91 Quantum Key Distribution: Entangled-Pair CHSH Test

The E91 protocol distributes a secret key using entangled photon pairs instead of single prepared photons: Alice and Bob each choose one of three random analyzer angles per pair, matching-angle rounds are sifted into an identical shared key, and the remaining rounds feed a live CHSH Bell-inequality calculation whose value certifies the channel's security. This simulation renders the entangled pairs traveling in 3D from a central source to Alice's and Bob's stations, flashing green or red for each ±1 outcome, while an adjustable intercept-resend eavesdropping attack visibly collapses the measured CHSH S value from the quantum maximum of 2√2 toward — and past — the classical limit of 2, and raises the sifted key's bit-error rate.