Security of quantum-key-distribution protocols using two-way classical communication or weak coherent pulses

We apply the techniques introduced by Kraus et al. [Phys. Rev. Lett. 95, 080501 (2005)] to prove security of quantum-key-distribution (QKD) schemes using two-way classical post-processing as well as QKD schemes based on weak coherent pulses instead of single-photon pulses. As a result, we obtain improved bounds on the secret-key rate of these schemes. For instance, for the six-state protocol using two-way classical post-processing we recover the known threshold for the maximum tolerated bit error rate of the channel, 0.276, but demonstrate that the secret-key rate can be substantially higher than previously shown. Moreover, we provide a detailed analysis of the Bennett-Brassard 1984 (BB84) and the SARG protocol using weak coherent pulses (with and without decoy states) in the so-called untrusted-device scenario, where the adversary might influence the detector efficiencies. We evaluate lower bounds on the secret-key rate for realistic channel parameters and show that, for channels with low noise level, the bounds for the SARG protocol are superior to those for the BB84 protocol, whereas this advantage disappears with increasing noise level.

Figure 1

(Color online) Lower bound on the secret-key rate per pulse and optimal $\mu$ for Poissonian sources as a function of the distance, for the BB84 and SARG protocols, when Alice and Bob share a quantum channel with perfect visibility $V=1$. The other experimental parameters are $\alpha =0.25\mathrm{dB}∕\mathrm{km}$, ${\eta }_{\det }=0.1$, and $p_d={10}^{-5}$. The thick lines are the results we obtain when Alice performs an optimal bitwise local randomization; the thin lines are the same, without randomization $(q=0)$.

Figure 2

(Color online) Same plot as in Fig. 1 (top), but for a quantum channel with nonperfect visibility, $V=0.95$.

Figure 3

(Color online) Lower bound on the secret-key rate per pulse and optimal $\mu$ for Poissonian sources as a function of the distance, for the BB84 and SARG protocols using decoy states, when Alice and Bob share a quantum channel with perfect visibility $V=1$. The other parameters are the same as in Fig. 1. The thick lines are the results we obtain when Alice performs an optimal bitwise local randomization; the thin lines correspond to the protocol without randomization $(q=0)$.

Figure 4

(Color online) Same plots as in Fig. 3, but for a quantum channel with nonperfect visibility, $V=0.95$.