A source emits entangled photon pairs in the singlet state |ψ⁻⟩ = (|01⟩ − |10⟩)/√2. Alice and Bob each independently pick one of three analyzer angles at random for every pair:
Alice: a1=0° a2=45° a3=90°
Bob: b1=45° b2=90° b3=135°
Quantum mechanics predicts a correlation between the ±1 outcomes that depends only on the angle difference:
E(θa,θb) = ⟨rA·rB⟩ = −cos(θa − θb)
- Key generation — when the bases happen to match (a2 with b1, or a3 with b2), the outcomes are perfectly anti-correlated (Δ=0° → E=−1). Bob flips his bit and the two share an identical, secret random bit — no basis-reconciliation broadcast reveals the bit itself, only which rounds matched.
- Security test (CHSH) — the remaining, non-matching angle pairs are used to evaluate S = |E(a1,b1) − E(a1,b3) + E(a3,b1) + E(a3,b3)|. An ideal, unmeasured entangled pair gives S = 2√2 ≈ 2.828 (the Tsirelson bound), strictly above the S ≤ 2 limit any local-hidden-variable / classical strategy can reach.
- Eavesdropping — an intercept-resend attack forces Eve to measure (and thus collapse) each tapped pair in some basis before forwarding it. This destroys the entanglement for that pair: S drifts down toward — and eventually below — 2, and the sifted key develops a measurable bit-error rate (QBER). Both signal a compromised channel, and Alice and Bob abort instead of using the key.
- Peve slider — the fraction of pairs Eve intercepts; higher values collapse S faster and raise the QBER.
This is the mechanism proposed by Artur Ekert in 1991 (E91): unlike prepare-and-measure schemes such as BB84, its security is certified directly by a live Bell-inequality violation rather than by an assumption about the source.