Secure bound of quantum key distribution with nonuniform random seed in privacy amplification
Phys. Rev. A 113, 052612 – Published 15 May, 2026
DOI: https://doi.org/10.1103/yt69-p1qj
Abstract
In the domain of quantum key distribution (QKD), the establishment of secure communication channels relies on the comprehensive analysis of the secure bounds. However, the impact of nonuniform random numbers in privacy amplification on secure bounds has rarely been discussed. This work proposes a more comprehensive analysis method for the secure bounds of practical QKD systems with imperfect random numbers in privacy amplification (PA) . We expand the quantum leftover hash lemma to the case of nonuniform random numbers and prove its security based on the min-entropy. Following this, we derive a revised secure bound for practical QKD systems. Using the two-decoy-state BB84 protocol as an example, we simulate the impact of imperfect random numbers in privacy amplification on the secure bounds of a QKD system. The simulation results indicate that the secure bound will be seriously affected when the average min-entropy of random numbers is below 0.95. These findings theoretically validate the necessity of using distilled uniform random numbers in PA, providing practical guidance for mitigating potential loopholes in practical QKD systems caused by imperfect random numbers.
