Efficient Quantum Key Distribution Scheme And Proof of Its Unconditional   Security
  We devise a simple modification that essentially doubles the efficiency of the BB84 quantum key distribution scheme proposed by Bennett and Brassard. We also prove the security of our modified scheme against the most general eavesdropping attack that is allowed by the laws of physics. The first major ingredient of our scheme is the assignment of significantly different probabilities to the different polarization bases during both transmission and reception, thus reducing the fraction of discarded data.   A second major ingredient of our scheme is a refined analysis of accepted data: We divide the accepted data into various subsets according to the basis employed and estimate an error rate for each subset *separately*.   We then show that such a refined data analysis guarantees the security of our scheme against the most general eavesdropping strategy, thus generalizing   Shor and Preskill's proof of security of BB84 to our new scheme. Up till now, most proposed proofs of security of single-particle type quantum key distribution schemes have relied heavily upon the fact that the bases are chosen uniformly, randomly and independently. Our proof removes this symmetry requirement. 
Hoi-Kwong Lo (University of Toronto), H. F. Chau (University of Hong   Kong) and M. Ardehali