User:FiberOptix/E 91 Quantum Cryptographic Protocol

The Ekert scheme is a variation of the BB84 protocol. Instead of using a quantum channel carrying two qubits from Alice to Bob, a channel is instead used carrying two qubits from one common source using Einstein-Podolsky-Rosen entangled photon pairs with one photon going to Alice and the other to Bob. When a reliable source is used, the E91 protocol reduces to that of BB84 as illustrated below.

The source emits two qubits in the same state chosen randomly among the four states of the BB84 protocol. Both Alice and Bob independently measure their qubit randomly in one of the two possible bases. After Alice and Bob have measured their qubits the source then announces the bases and Alice and Bob discard any qubits chosen where they haven’t selected in the announced basis – about 50%. Just as in the BB84 protocol, Alice and Bob compare a subset of the remaining key over a public channel and discard if they find any disagreement. Relying on the fact that the emitted particles are in a maximally entangled state, the security of the system is not compromised if the source falls into Eve’s hands.

This variation of the BB84 protocol is of special conceptual, historical, and practical interest. The idea is due to Artur Ekert (1991) of Oxford University, who, while elaborating on a suggestion of David Deutsch (1985), discovered QC independently of the BB84 paper. Intellectually, it is very satisfying to see this direct connection to the famous EPR paradox (Einstein, Podolski, and Rosen, 1935): the initially philosophical debate turned to theoretical physics with Bell’s inequality (1964), then to experimental physics (Freedmann and Clauser, 1972; Fry and Thompson, 1976; Aspect et al., 1982), and is now— thanks to Ekert’s ingenious idea—part of applied physics.