Unconditional Security of the Bennett 1992 quantum key-distribution over lossy and noisy channel

We show that the security proof of the Bennett 1992 protocol over loss-free channel in (K. Tamaki, M. Koashi, and N. Imoto, Phys. Rev. Lett. 90, 167904 (2003)) can be adapted to accommodate loss. We assumed that Bob's detectors discriminate between single photon states on one hand and vacuum state or multi-photon states on the other hand.Comment: 5 pages, 2 figures. We have presented this topic at QIPC 2003 as a poster sessio