Quantum Bit Error Rate Analysis in BB84 Quantum Key Distribution: Measurement, Statistical Estimation, and Eavesdropping Detection

Abstract

Quantum Key Distribution (QKD) provides information-theoretic security by exploiting the principles of quantum mechanics. Among QKD protocols, the BB84 scheme remains the most widely adopted for both theoretical research and practical implementation. A critical parameter determining the reliability and security of BB84 is the Quantum Bit Error Rate (QBER), which quantifies errors in the sifted key arising from channel noise or potential eavesdropping. This paper presents a systematic review and analysis of QBER within the BB84 protocol, examining its calculation, statistical estimation methods, and role in detecting eavesdropping activity. Simulation results, corroborated by reported experimental observations, reveal a near-linear relationship between eavesdropping intensity and QBER, with values approaching 25% under full intercept-resend attacks. Four confidence interval estimation methods, Wald, Wilson, Clopper-Pearson, and Hoeffding's inequality, are compared for robust QBER analysis in finite-key scenarios. Protocol enhancements, including decoy-state methods, hybrid cryptographic models, and quantum-resistant authentication, are discussed as mechanisms to mitigate errors and strengthen resilience across fiber, free-space, underwater, and satellite QKD systems. Open challenges in distinguishing noise-induced errors from malicious eavesdropping, and the role of adaptive error correction and machine-learning-assisted QBER estimation in future quantum networks, are identified as key directions for further research.

Figures (4)

• Figure 1: Flowchart of the BB84 quantum key distribution protocol.
• Figure 2: QBER as a function of Eve's interception fraction (simulation results). Each point represents the mean QBER over 50 independent trials with $n = 50{,}000$ sifted bits (seed = 42). The shaded band represents 95 % confidence intervals computed via normal approximation Renner_2008. Results confirm the near-linear relationship between eavesdropping intensity and QBER, approaching 25 % under full intercept--resend attack, consistent with the theoretical prediction $Q = f/4$Bennett_2014Lo_1999. Numerical values for selected interception fractions are listed in Table \ref{['tab:qber_results']}.
• Figure 3: QBER distribution with no eavesdropper present. All 50 simulation trials ($n = 50{,}000$ sifted bits each, seed = 42) yield $\mathrm{QBER} = 0.000$, demonstrating that error-free key generation is achievable under ideal, attack-free conditions. This result corresponds directly to the $f = 0$ data point in Fig. \ref{['fig:qber_sim']} and Table \ref{['tab:qber_results']}.
• Figure 4: QBER distribution under a full intercept--resend attack ($f = 1.0$). The histogram shows the distribution of QBER values across 50 independent simulation trials ($n = 50{,}000$ qubits each, seed = 42). The distribution is tightly centred at mean $= 0.2495$, consistent with the theoretical prediction $Q = f/4 = 0.250$Bennett_2014Lo_1999 and the value reported in Table \ref{['tab:qber_results']}. The narrow spread (std $= 0.0023$) reflects the large sample size. The dashed line marks the theoretical limit. Compare with Fig. \ref{['fig:qber_no_eve']}, where $f = 0$ yields $\mathrm{QBER} = 0$ across all trials.