E91 Protocol

An entanglement-based quantum key distribution protocol using Bell inequality violations for security.

E91 is a QKD protocol proposed by Artur Ekert in 1991. Unlike BB84, it uses entanglement and Bell inequalities to guarantee security.

The Key Idea

Alice and Bob share entangled photon pairs. By measuring Bell inequality violations, they can verify:

A source produces Bell pairs: $∣ Ψ^{-} ⟩ = \frac{1}{2} (∣01 ⟩ - ∣10 ⟩)$

One photon goes to Alice, one to Bob.

For each photon pair:

Alice and Bob announce their measurement choices (not results).

When Alice chose $A_{1}$ and Bob chose $B_{3}$ , or Alice chose $A_{3}$ and Bob chose $B_{1}$ :

Use other combinations ( $A_{1} B_{1}$ , $A_{2} B_{1}$ , $A_{2} B_{2}$ , $A_{3} B_{2}$ ) to compute CHSH:

$S = E (A_{1}, B_{1}) - E (A_{1}, B_{2}) + E (A_{2}, B_{1}) + E (A_{2}, B_{2})$

The key insight: Bell violations certify quantum correlations.

If Eve intercepts and resends, she breaks the entanglement, reducing Bell violation. Alice and Bob detect this as reduced $S$ value.

Source can be untrusted: Even if Eve controls the source, Bell violations prove security
Path to device-independence: Foundation for Device-Independent QKD (DI-QKD)
Symmetric: Neither party needs to trust the source