Practical issues in decoy-state quantum key distribution based on the central limit theorem

Decoy-state quantum key distribution (QKD) is a standard tool for long-distance quantum communications. An important issue in this field is processing the decoy-state statistics taking into account statistical fluctuations (or “finite-key effects”). In this work, we propose and analyze an option for decoy statistics processing, which is based on the central limit theorem. We discuss such practical issues as inclusion of the failure probability of the decoy-state statistical estimates in the total failure probability of a QKD protocol and also taking into account the deviations of the binomially distributed random variables used in the estimations from the Gaussian distribution. The results of numerical simulations show that the obtained estimations are quite tight. The proposed technique can be used as a part of post-processing procedures for industrial quantum key distribution systems.

Figure 1

Comparison of the proposed parameter estimation procedure with the theoretical limit for relevant parameters of the QKD setup. In (a) sifted and secret keys rates are presented as functions of the communication distance. In (b) the optimized intensities for signal and decoy states, together with optimized intensity for signal states in the limit case, are shown as functions of the communication distance. In (c) the optimized fraction of decoy-state probabilities as functions of the communication distance are given. We note that the fraction of signal states is given by $p_{\mu }=1-(p_{\nu }+p_{\lambda })$.

Figure 2

Total number of transmitted pulses $N$ and length of verified key $l_{\mathrm{ver}}$ as functions of the communication distance. In the inset the value of QBER is shown as a function of the communication distance.