  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.
