Theoretical and simulation investigation of practical QKD for both BB84 and SARG04 protocols

In this paper, we provide a simple approach for determining the rate of secure key production when single-photon and two-photon pulses are used to generate the secure key. For both BB84 and SARG04, we offer estimation and optimization of decoy-state parameters for a single decoy state protocol and two decoy state protocols. This method can be used to determine the lower bound on the fraction of single-photon counts (y(1)), the fraction of two-photon counts (y(2)), the upper bound on the QBER of single-photon pulses (e(1)), the upper bound on the QBER of two-photon pulses (e(2)), and the lower bound on the key generation rate for both BB84 and SARG04. Due to the limited data size in real-world experiments, we estimate the statistical fluctuations of several parameters, including the gain and QBER of the signal state, as well as the gain and QBER of the decoy state, which are used to estimate the lower bound of key generation rate. We propose formulae that specify the optimal decoy and signal state percentages and intensities. Then we can determine the maximum and optimal key generation rate. For both SARG04 and BB84, we simulated a free space-based QKD system using our decoy state strategy. The simulation results show that free space-based QKD systems that use the suggested approach for BB84 can achieve a higher secret key rate and a greater safe distance than SARG04-based systems.