Improvement of the safe transmission distance via optimization of the photon number distribution for the faint optical pulse in practical quantum key distribution systems

With practical quantum key distribution (QKD) systems, estimating the safe transmission distance and the safe bit rate under some transmission distance is quite important. For the practical QKD setup, with decoy states, the photon count distribution of the faint laser pulse with signal states can be optimized to acquire the maximum transmission distance. With this goal, we implement a method combining mathematical derivation and numerical simulation to find the optimal photon count distribution under realistic conditions; the numerical simulation results show that the new distributions can be employed in the decoy QKD system to reach safe transmission distances farther than those reached by systems with the Poisson distribution.