Paper [8] in the QKD Krylov Detector research series. We validate the Calibrated Slope Detector on 181,606 experimental QBER measurements from a real fiber-optic QKD system. The detector achieves a false-positive rate of 4.5% and detects simulated intercept-resend attacks from ΔQBER ≥ 0.5% with 96.0% sensitivity (AUC = 0.981) — an order of magnitude more sensitive than conventional QBER threshold monitoring. Supplementary validation on the NIST Loophole-Free Bell Test dataset (152.6 million trials) confirms specificity on clean quantum data. This completes the validation triangle: theoretical unforgeability (Paper [7]), simulation-based sensitivity (Papers [5]–[6]), and real-data validation (this work). Software: https://github.com/quantumspiritresearch-crypto/qkd-krylov-detector (v1.3.0)
Paper [8] in the QKD Krylov Detector research series. We validate the Calibrated Slope Detector on 181,606 experimental QBER measurements from a real fiber-optic QKD system. The detector achieves a false-positive rate of 4.5% and detects simulated intercept-resend attacks from ΔQBER ≥ 0.5% with 96.0% sensitivity (AUC = 0.981) — an order of magnitude more sensitive than conventional QBER threshold monitoring. Supplementary validation on the NIST Loophole-Free Bell Test dataset (152.6 million trials) confirms specificity on clean quantum data. This completes the validation triangle: theoretical unforgeability (Paper [7]), simulation-based sensitivity (Papers [5]–[6]), and real-data validation (this work). Software: https://github.com/quantumspiritresearch-crypto/qkd-krylov-detector (v1.3.0)
Abstract I present a physical-layer monitoring framework for quantum key distribution (QKD) implementations based on Krylov/operator-growth diagnostics. Running alongside standard parameter estimation, privacy amplification, and composable security proofs, it addresses a focused question: whether the temporal correlation structure of an observed quantum bit error rate (QBER) stream carries additional information about physical channel perturbations. Within a specified local-Hamiltonian channel model, the Lanczos coefficients of the channel Liouvillian define an operator-growth autocorrelation template, and deviations from it serve as anomaly scores for implementation monitoring. For the model studied here, the QBER autocorrelation relates to the operator autocorrelation through a proportionality relation, CQBER(τ)=α(N)Cop(τ) C QBER ( τ ) = α ( N ) C op ( τ ) , with α(N) α ( N ) an explicitly specified calibration factor. Local Hamiltonian perturbations generically distort the associated Krylov fingerprint once the perturbation reaches the support of the monitored observable, consistent with the locality of the Lanczos recursion and with Lieb–Robinson bounds. The resulting three-layer pipeline combines adaptive frequency filtering, Krylov-template extraction, and calibrated slope detection. On simulated BB84-like QBER data with realistic hardware noise, the detector achieves high anomaly discrimination under the tested perturbation classes ( AUC=0.9899 AUC = 0.9899 ). On 181,606 181 , 606 public QBER measurements from a deployed fiber-optic QKD system, it yields a 4.5% clean-test alarm rate against a 5% design target and detects injected perturbations with 96.0% sensitivity at ΔQBER=+0.5% Δ QBER = + 0.5 % ( AUC=0.981 AUC = 0.981 ). Certification of final key secrecy remains governed by the underlying QKD protocol, parameter estimation, finite-key analysis, and privacy amplification.
This collection presents three interconnected papers on eavesdropper (Eve) detection in Quantum Key Distribution (QKD) channels, following the chronological development of the framework. Part I Eve Detection in QKD via Dual-Layer Sidereal Filtering and Krylov Complexity Analysis (v4): The empirical starting point. Eve is modeled as a Hamiltonian perturbation at the kappa-coupling interface. Krylov-Statistical Mapping establishes a correlation between b_n deviation and QBER statistical moments (r=0.948, kurtosis; r=0.943, |skewness|) across 50 gamma values. Crossover spectral regime (⟨r⟩=0.366) explicitly documented. Part II: Distinguishing Quantum Scrambling from Eavesdropping via Krylov Temporal Structure and Sidereal Filtering (v2, with Robustness Analysis): The theoretical foundation. A Gaussian autocorrelation template C(t) = exp(−0.5·(slope·t)²) is derived from Krylov-Lanczos b_n coefficients. Under realistic hardware noise (AR(1) + 1/f + afterpulsing + bursts): AUC=0.9899, separation=12.13 sigma. Three methodological killer tests included. All results are simulation-based (N=8 crossover regime; not yet validated on real QKD hardware). Part III: QKD Eve Detector: A Unified Framework (Synthesis): The three-layer detector combining all prior work: (1) Dual-Layer Sidereal Filter for environmental noise removal, (2) Krylov Dynamic Detector for template matching, (3) Multi-Vector Attack Classifier distinguishing six attack types. Self-contained implementation provided in the accompanying demo notebook.Accompanying notebooks reproduce all figures and results. Dependencies: NumPy, SciPy, QuTiP. No special hardware required.
We develop a rigorous mathematical framework proving that the QKD Krylov Detector, a three-layer eavesdropper detection system for Quantum Key Distribution based on Krylov complexity and sidereal filtering, provides information-theoretically grounded security against physically realizable attacks. The central results are: (1) Krylov Locality Theorem: An eavesdropper coupling at distance d from the monitored operator cannot affect the first d Lanczos coefficients. This is an exact algebraic identity, not an approximation. (2) Perturbation Detectability Theorem: The first affected Lanczos coefficient scales as gamma^2, with computable upper and lower bound constants derived from second-order perturbation theory applied to the Lanczos recursion. (3) Information-Distortion Bound: Eve's accessible information (Holevo quantity) scales as O(gamma^2), while the Krylov distortion scales as O(gamma^4), yielding an explicit tradeoff chi <= const * sqrt(Delta_K). Verified numerically using an explicit Eve ancilla model. (4) Krylov Unforgeability Theorem: Any Hamiltonian perturbation that extracts nonzero information from the quantum channel necessarily distorts the Lanczos coefficients beyond the detection threshold. No physically realizable attack can simultaneously extract information and preserve the clean Krylov signature. (5) Coherent Attack Invariance: The Lanczos coefficients are operator-space quantities independent of any quantum state, rendering coherent and entangled attack strategies unable to circumvent detection. (6) Time-Dependent Unforgeability: Time-dependent coupling strategies gamma(t) produce strictly more distortion than constant coupling at the same average strength, by Jensen's inequality applied via a rigorous stroboscopic argument. All results include full proofs and numerical verification for chain lengths N = 6, 8, 10, 12. This work provides the formal security foundation for the QKD Krylov Detector framework developed across six prior publications. Companion code: https://github.com/quantumspiritresearch-crypto/qkd-krylov-detector
This work presents and evaluates two threshold-based detection methods for the Six-State quantum key distribution protocol, considering a realistic scenario involving partial intercept–resend attack and channel noise. The statistical properties of the shared quantum bit error rate (QBER) are analyzed and used to estimate the attacker interception density from observed data. Building on this foundation, the work derives two optimal QBER detection thresholds designed to minimize both false positive and false negative rates, following, respectively, upper theoretical bounds and limit probability density function approach. A developed Qiskit simulation environment enables the evaluation and comparison of the two detection methods on simulated and real-inspired quantum systems with differing noise characteristics. This framework moves beyond theoretical analysis, allowing practical investigation of system noise effects on detection accuracy. Simulation results confirm that both methods are robust and effective, achieving high detection accuracy across all the tested configurations, thereby validating their applicability to real-world quantum communication systems.
Abstract Secure military communications depend on the confidentiality of exchanged cryptographic keys across command centers, satellite links, and classified order transmission. Classical key-distribution protocols rely on computational hardness assumptions that provide no intrinsic mechanism for detecting interception; an adversary who copies transmitted ciphertext leaves no physical trace. Quantum Key Distribution (QKD), and specifically the BB84 protocol, replaces this assumption with a physical guarantee derived from quantum mechanics: any attempt to measure an unknown quantum state necessarily disturbs it, rendering interception statistically detectable. This study implements the BB84 protocol at the circuit level — qubit state preparation, basis selection, interception modeling, and measurement — and validates its central security property, the Quantum Bit Error Rate (QBER) signature of eavesdropping, in two stages: (1) a noiseless statevector simulation using the PKTron quantum computing framework over ten independent trials per condition, and (2) hardware execution on IBM Quantum's ibm_fez superconducting processor. In simulation, the average QBER without an eavesdropper was 0.000, and with a full intercept-resend attack was 0.248, closely matching the theoretical prediction of 0.25. On real hardware, the undisturbed channel returned QBER = 0.000 (19 sifted bits) and the eavesdropped channel returned QBER = 0.261 (23 sifted bits), in close agreement with both theory and the simulated baseline. These results provide a reproducible, two-platform validation of the eavesdropper-detection mechanism that underlies the security claims made for QKD-protected communications. This study validates the cryptographic detection primitive only; it does not constitute a deployed secure communications system, and extending these results to operational command, satellite, or classified-order channels requires physical single-photon transmission hardware, authenticated classical channels, and full key-management infrastructure outside the scope of this work.
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.