Abstract

Recently, a scheme for the generation of bright entangled beams has been suggested [1]. The EPR-like quantum correlations are produced by letting two amplitude-squeezed bright optical fields interfere on a 50:50 beamsplitter. Fig. 1 illustrates it in phase space representation in a single-mode picture. The phase (PM) and amplitude (AM) uncertainty measurements exhibit strong correlations and anticorrelations which can be detected by recording the difference (sum) of the PM (AM) photocurrents. The simple version of the quantum key distribution protocol works as follows. Alice and Bob assign bit values ”0” and ”1” to the choice of a measured variable, PM or AM. The source of bright entangled beams is at Alice’s station. She keeps output 1 of Fig. 1 at her station and sends output 2 to Bob. Bob performs at random AM or PM and records the bit value and the corresponding time slot. Alice performs her measurements parallel to Bob, also making a random choice of a measured variable and recording it. Bob sends the results of his measurements, a photocurrent signal, down the classical channel back to Alice. Alice detects the difference of her and Bob’s signal, if she used PM and sum for AM. In the absence of an eavesdropper and for high-degree squeezing and hence high-quality entanglement, the difference (sum) signal drops to zero. Alice tells Bob, in which time slots she sees correlations and hence her and Bob’s choices of a measured variable coincide. Out of them Alice and Bob create a key string. The invasion of Eve would be immediately disclosed as the correlations are distorted. In view of Eve’s guessing strategy the protocol can be extended. Alice introduces at random a rotation of uncertainty region by ±ϕ, say ±π/4, in one of the outputs, thus destroying the correlations. Correlations can be recovered by applying an inverse rotation. This decreases the key rate. However, the error rate introduced by a potential eavesdropper is increased as Eve has to make the right guess of AM or PM and ±ϕ The security of the protocol is guaranteed by both the Heisenberg uncertaity relation and the continuous EPR correlations. The suggested scheme seems to be more tolerable to the realistic limitations in the quality of entanglement and to losses than the known continuous variable cryptography schemes [2]. It was checked for Eve applying a QND measurement of both amplitude and phase and for Eve’s guessing strategy. The implementation of the protocol, at least in its simple version, is experimentally less cumbersome if compared to [2]. For instance, amplitude-squeezed fiber optical solitons can be employed [1] to provide reliable and efficient entangled source. We believe that the suggested scheme provides an efficient and novel approach to continuous variable quantum communication. This work is supported by Deutsche Forschungsgemeinschaft.

© 2000 IEEE