Efficient quantum-key-distribution scheme with nonmaximally entangled states

We propose an efficient quantum-key-distribution scheme based on entanglement. The sender chooses pairs of photons in one of the two equivalent nonmaximally entangled states randomly, and sends a sequence of photons from each pair to the receiver. The sender and receiver choose from the various bases independently but with substantially different probabilities, thus reducing the fraction of discarded data, and a significant gain in efficiency is achieved. We then show that refined data analysis like that proposed by Lo et al. (H. K. Lo, H. F. Chau, and M. Adrehali, e-print quant-ph/0011056) guarantees the security of our scheme against a biased eavesdropping strategy. Remarkably, our scheme is more efficient than distillation of singlets out of the nonmaximally entangled states and biased detection afterward.