Quantum key distribution without alternative measurements

Entanglement swapping between Einstein-Podolsky-Rosen ~EPR! pairs can be used to generate the same sequence of random bits in two remote places. A quantum key distribution protocol based on this idea is described. The scheme exhibits the following features. ~a! It does not require that Alice and Bob choose between alternative measurements, therefore improving the rate of generated bits by transmitted qubit. ~b! It allows Alice and Bob to generate a key of arbitrary length using a single quantum system ~three EPR pairs!, instead of a long sequence of them. ~c! Detecting Eve requires the comparison of fewer bits. ~d! Entanglement is an essential ingredient. The scheme assumes reliable measurements of the Bell operator. PACS number~s!: 03.67.Dd, 03.67.Hk, 03.65.Bz The two main goals of cryptography are for two distant parties, Alice and Bob, to be able to communicate in a form that is unintelligible to a third party, Eve, and to prove that the message was not altered in transit. Both of these goals can be accomplished securely if both Alice and Bob are in possession of the same secret random sequence of bits, a ‘‘key’’ @1#. Therefore, one of the main problems of cryptography is the key distribution problem, that is, how do Alice and Bob, who initially share no secret information, come into the possession of a secret key, while being sure that Eve cannot acquire even partial information about it. This problem cannot be solved by classical means, but it can be solved using quantum mechanics @2#. The security of protocols for quantum key distribution ~QKD! such as the BennettBrassard 1984 ~BB84 !@ 2#, E91 @3#, B92 @4#, and other protocols @5,6#, is assured by the fact that while information stored in classical form can be examined and copied without altering it in any detectable way, it is impossible to do that when information is stored in unknown quantum states, because an unknown quantum state cannot be reliably cloned ~‘‘no-cloning’’ theorem @7#!. In these protocols security is assured by the fact that both Alice and Bob must choose randomly between two possible measurements. In this paper I introduce a QKD scheme which does not require that Alice and Bob choose between alternative measurements. This scheme is based on ‘‘entanglement swapping’’ @8‐10# between two pairs of ‘‘qubits’’ ~quantum two-level systems!, induced by a Bell operator measurement @11#. The Bell operator is a nondegenerate operator which acts on a pair of qubits i and j, and projects their combined state onto one of the four Bell states