 chances X|+> = l+> bk = 0, 1 Eigenvalue +1, bk = 0 rest of the B92 protocol follows the same path as that of BB84, i.e., using information reconciliation and privacy amplification or SKD. 25.12 The EPR protocol The EPR protocol, named after entangled EPR pairs or Bell states (see Chapter 16) was invented by A. K. Eckert in 1991. The idea is that Alice and Bob share, over a quantum channel, an ensemble of N = (4 + A) n such EPR pairs, based, for instance, on one of the four EPR-Bell states:22 1800)==100)+1111 (25.28) Prior to any measurement, the quantum state of Alice's and Bob's system is, thus, defined by the N-EPR tensor: (25.29) As with previous protocols, Alice and Bob use random-bit generators to produce bit sequences A = (a1,a2, . . ) and A' = (a', a'2, ,...a), of length N = (4 + A) n bits. The bit values ak, a'k determine their choice of measurement basis, for instance Z for ak = 0 (Alice's side) or a'k = 0 (Bob's side), and X in the other case, as applicable to the first (Alice) and second (Bob) qubits, respectively, of any of the EPR pairs from the above N-EPR tensor. The cbit outcomes of Alice or Bob measurements generate random bit sequences B = (b1, ,b2,...,bn) and B = (b1,b,..., , b'N), respectively. EPR-Bell states can be physically generated through pairs of entangled photons. See, for instance: http://physicsworld.com/cws/article/print/11360/1/smallphotons, p://physicsworld.com/cws/article/news/24358, www.quantum.at/research/quantum-teleportation-communication-entanglement/ entangled-photons-over-144-km.html Classical and quantum cryptography How does an eigenvalue measurement with X or Z apply in the case of a single EPR pair, such as |Boo)? The answer is simple, if one considers that the entangled state can also be written in the form23 (25.30) If Alice uses X for her first qubit measurement of 1Boo), she obtains equally likely eigenvalues +1 with corresponding post-measurement or collapsed states /V/B = 1+) or |-), and cbits bk = 0 or bk = 1, respectively (using the same convention as in B92)