Finite-key-size security of the Phoenix-Barnett-Chefles 2000 quantum-key-distribution protocol

The postselection technique was introduced by Christandl, König, and Renner [Phys. Rev. Lett. 102, 020504 (2009)] in order to simplify the security of quantum-key-distribution schemes. Here, we present how it can be applied to study the security of the Phoenix-Barnett-Chefles 2000 trine-state protocol, a symmetric version of the Bennett 1992 protocol.

Figure 1

Upper bounds on the secret-key fraction $r$ for the finite PBC00 protocol as a function of the exchanged quantum signals $N$ for bit-error rates $Q=0.5\%$, 2%, 2.5%, 5%. The maximum failure probability of the protocol is $\varepsilon ={10}^{-5}$ and the failure probability of the error-correction procedure is ${\varepsilon }_{\mathrm{EC}}={10}^{-10}$.

Figure 2

Upper bounds on the secret-key fraction $r$ for the finite PBC00 protocol as a function of the exchanged quantum signals $N$ for bit-error rate $Q=2.5\%$, $\varepsilon ={10}^{-5}$, and ${\varepsilon }_{\mathrm{EC}}={10}^{-10}$ for (a) collective attacks (b) postselection technique.