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.
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.
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.
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
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)
We propose that quantum scrambling in many-body quantum channels constitutes a cryptographic resource that enables a fundamentally new class of channel authentication protocols. By synthesizing results from three independent lines of investigation, scrambling irreversibility in closed quantum systems, Krylov complexity-based channel detection, and sidereal filtering validated on real astrophysical data, we establish the following chain of reasoning. First, scrambling in symmetry-broken Heisenberg chains produces a practically irreversible dynamical process, with Poincaré recurrence times scaling as τ_rec ~ (1/ε)^{2^N - 1}. Second, the Lanczos coefficients b_n of the channel Hamiltonian determine the functional form of the channel's temporal autocorrelation through the dynamical susceptibility, yielding a Gaussian template for linearly growing b_n. Third, in simulated experiments using template-matching classifiers applied to scrambling-derived correlation traces, compromised channels can be distinguished from clean channels with an area-under-curve (AUC) value of 0.99 under controlled realistic noise conditions. Fourth, as a proof-of-concept for extracting stable temporal fingerprints from noisy real-world signals, the sidereal filtering layer has been validated on 59,389 pulsar time-of-arrival measurements from the NANOGrav 15-year dataset. We argue that the combination of these results implies that scrambling defines a physical one-way signature: a measurable, predictable, and practically unforgeable channel fingerprint whose security rests on quantum-mechanical irreversibility rather than computational hardness assumptions. This work synthesizes and extends the author's prior publications on sidereal filtering, scrambling dynamics, and the QKD Eve Detector framework, connecting them into a unified cryptographic paradigm.
We establish a formal and numerical connection between the Krylov-based eavesdropper detector for quantum key distribution (QKD) and the Loschmidt echo. We introduce the operator-space Loschmidt echo M_op(t) and show analytically that the Krylov detection score is equivalent to the time-averaged operator echo. Numerical simulations on an 8-qubit Heisenberg chain with N=20 coupling strengths confirm this equivalence: gamma^2 vs. Lanczos distortion (r=0.958, p<1e-10), echo decay vs. Lanczos distortion (r=0.838, p<1e-5), and Krylov score vs. echo decay (r=0.850, p<1e-5). The operator-space echo decays faster than the state-space echo, explaining why the Krylov detector is more sensitive than state-based fidelity measures. These results connect the Krylov QKD framework to experimental Loschmidt echo platforms (NMR, ultracold atoms, superconducting qubits). Includes reproducible Python code and all numerical data.
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.