Numerical Analysis of Quantum Bit Error Rate and Secure Key Rate under Realistic Communication Parameters

Abstract

This paper aims to discuss the role of security parameters-Secure Key Rate and Quantum Bit Error Rate (QBER) in a framework of a BB84 protocol and how they perform under the presence of simulative physical imperfections. The approximations on the framework also show how an upper bound of SKR can be calculated. The dependence of QBER on channel distance and optical error is presented, indicating that QBER is approximately the error rate at lower distance. Further increase in distance causes rapid increase in QBER with saturation at 50% at high distances. The SKR, on the other hand, decrease with distance while the upper bound of SKR remains constant till a certain distance where they become null. The linear relationship of SKR was also depicted. The plot of SKR vs Mean photon number reveals the range of mean photon number- 0.4 to 0.8 where SKR achieve their maximum value. The plots of upper and lower bounds of SKR with respect to optical error rate indicating the logarithmic decay of SKR for slight increase in optical error. © 2026 IEEE.