Unconditional Security of the Bennett 1992 quantum key-distribution protocol over a lossy and noisy channel
by
Kiyoshi Tamaki
Perimeter Institute for Theoretical Physics
Coauthors: Masato Koashi, Norbert Luetkenhaus, Nobuyuki Imoto

We study the unconditional security of the Bennett 1992 quantum key-distribution protocol (B92) over a lossy and noisy channel. For the simplicity of the analysis, we assume that Alice encodes bit values into the single photon polarization state, and Bob's detectors discriminate between single photon states on one hand and vacuum state or multi-photon states on the other hand. To prove the security, we first propose an unconditionally secure protocol that employs the entanglement distillation protocol (EDP) based on a filtering operation and the Calderbank-Shor-Steane (CSS) quantum error correcting codes. The bit errors and the phase errors, which have to be estimated for the EDP based protocol, are correlated after the filtering operation, and we can bound the phase error rate from the observed bit error rate by an estimation method involving nonorthogonal measurements. By showing the equivalence between this EDP based protocol and the B92, we have proven the unconditional security of the B92.

Date received: April 22, 2004