Realistic detector model for a time-bin-encoding quantum key distribution system

In light of the growing widely utilized single-photon avalanche detectors, dead time is inevitable due to the presence of afterpulse. Dead time is a critical factor that influences the count rate and the secret key rate (SKR) of quantum key distribution (QKD). It is particularly significant in time-bin-encoding systems, while prior models fail to accurately estimate the gains. Of note, it introduces correlations between early bins and late bins, hence bits with strong correlation and security risks. Here, we put forward a realistic model that precisely characterizes the response of detectors for time-bin-encoding systems. Our model not only improves the accuracy of gain predictions, showing an excellent match with the Monte Carlo simulation results, but also provides theoretical support for data processing, helping to mitigate security risks. Finally, leveraging our model, we can get a much higher SKR than prior models and further enhance the performance of practical QKD systems by adjusting the detector parameters. Our simulation results demonstrate that our model is essential for the application and deployment of QKD systems in practice.