Performance of two quantum-key-distribution protocols

We compare the performance of Bennett-Brassard 1984 (BB84) and Scarani-Acin-Ribordy-Gisin 2004 (SARG04) protocols, the latter of which was proposed by V. Scarani et al. Phys. Rev. Lett. 92, 057901 (2004). Specifically, in this paper, we investigate the SARG04 protocol with two-way classical communications and the SARG04 protocol with decoy states. In the first part of the paper, we show that the SARG04 scheme with two-way communications can tolerate a higher bit error rate (19.4% for a one-photon source and 6.56% for a two-photon source) than the SARG04 one with one-way communications (10.95% for a one-photon source and 2.71% for a two-photon source). Also, the upper bounds on the bit error rate for the SARG04 protocol with two-way communications are computed in a closed form by considering an individual attack based on a general measurement. In the second part of the paper, we propose employing the idea of decoy states in the SARG04 scheme to obtain unconditional security even when realistic devices are used. We compare the performance of the SARG04 protocol with decoy states and the BB84 one with decoy states. We find that the optimal mean-photon number for the SARG04 scheme is higher than that of the BB84 one when the bit error rate is small. Also, we observe that the SARG04 protocol does not achieve a longer secure distance and a higher key generation rate than the BB84 one, assuming a typical experimental parameter set.