A Validated and Reproducible Monte Carlo Baseline for the BB84 Protocol Under Depolarizing Channel Noise

This study establishes a statistically rigorous and fully reproducible Monte Carlo bench- mark for the BB84 quantum key distribution (QKD) protocol under symmetric depolarizing channel noise. We implement a transparent, parameterized simulator to conduct extensive noise sweeps from p = 0% to p = 26% depolarizing probability. Through large-scale trials, each processing 104 signals with 10 independent repetitions, we generate statistically robust mean Quantum Bit Error Rate (QBER) and Shor-Preskill secure key rates, complete with 95% confidence intervals. Our results validate the fundamental Q p/2 relationship with a maximum deviation from theory of 0.27% and quantify the sharp security threshold collapse. At p = 10% (QBER ≈ 5%), we achieve an ideal asymptotic key rate of RQKD ≈ 0.427 per sifted bit, while the secure fraction becomes negligible beyond p = 22% (QBER ≈ 11%). The empirically determined threshold, where the secure key rate vanishes at pth 0.22, aligns closely with theoretical predictions. This work’s primary contribution is a validated computational framework that serves as an essential benchmark and a computational null hypothesis against which to quantify performance deviations in practical QKD systems aris- ing from reconciliation inefficiency, finite-key effects, and device imperfections, thus bridging a critical gap between asymptotic security theory and the engineering of real-world quantum networks.