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Quantum Scrambling as a Cryptographic Resource: From Krylov Complexity to Physical Channel Authentication

Daniel Süß

Published Mar 6, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.5281/zenodo.18889223

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A Comprehensive Review of Quantum Scrambling as a Cryptographic Resource in Quantum Key Distribution

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This review examines the preprint by Daniel Süß titled "Quantum Scrambling as a Cryptographic Resource: From Krylov Complexity to Physical Channel Authentication," which proposes quantum scrambling in many-body quantum channels as a novel cryptographic primitive for channel authentication in quantum key distribution (QKD). Key postulates include the irreversibility of scrambling dynamics, the role of Lanczos coefficients in determining channel autocorrelation signatures, and the practical unforgeability protected by doubly exponential Poincaré recurrence times. Hypotheses center on the deterministic, measurable, and secure nature of scrambling-derived fingerprints, validated through simulations and real astrophysical data from the NANOGrav dataset. Results demonstrate high detection accuracy (AUC = 0.99) under realistic noise. Similar research in quantum chaos, Krylov complexity, and QKD security is surveyed, highlighting ongoing trends toward physics-based cryptography amid quantum threats. Algebraic interpretations frame Krylov subspaces as orthogonal bases for operator evolution, while geometric views depict scrambling as diffusive spreading in operator space. The field is advancing toward hybrid quantum-classical protocols resilient to quantum attacks, potentially revolutionizing secure communications. Mamun, SM (2026)……………………………………1 A Comprehensive Review of Quantum Scrambling as a Cryptographic Resource in Quantum Key Distribution Also available on Academia.edu: https://www.academia.edu/attachments/132019982/download_file?s=portfolio

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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.
This review examines the preprint by Daniel Süß titled "Quantum Scrambling as a Cryptographic Resource: From Krylov Complexity to Physical Channel Authentication," which proposes quantum scrambling in many-body quantum channels as a novel cryptographic primitive for channel authentication in quantum key distribution (QKD). Key postulates include the irreversibility of scrambling dynamics, the role of Lanczos coefficients in determining channel autocorrelation signatures, and the practical unforgeability protected by doubly exponential Poincaré recurrence times. Hypotheses center on the deterministic, measurable, and secure nature of scrambling-derived fingerprints, validated through simulations and real astrophysical data from the NANOGrav dataset. Results demonstrate high detection accuracy (AUC = 0.99) under realistic noise. Similar research in quantum chaos, Krylov complexity, and QKD security is surveyed, highlighting ongoing trends toward physics-based cryptography amid quantum threats. Algebraic interpretations frame Krylov subspaces as orthogonal bases for operator evolution, while geometric views depict scrambling as diffusive spreading in operator space. The field is advancing toward hybrid quantum-classical protocols resilient to quantum attacks, potentially revolutionizing secure communications. Mamun, SM (2026)……………………………………1 A Comprehensive Review of Quantum Scrambling as a Cryptographic Resource in Quantum Key Distribution Also available on Academia.edu: https://www.academia.edu/attachments/132019982/download_file?s=portfolio
This paper closes three theoretical gaps that remained open in the Krylov-based quantum channel authentication framework developed across Papers 1-8 of this series. Physical Bridge (Theorem 1): I derive a formal proof that the QBER autocorrelation is proportional to the operator autocorrelation, C_QBER(τ) = α(N) · C_op(τ), establishing the connection between Krylov theory and observable measurement statistics (numerically confirmed with Pearson r = 0.9997). Physical One-Way Function (Theorem 2): I prove that the Krylov fingerprint map constitutes a physical one-way function with three independent hardness sources: (I) unconditional information-theoretic exponential ill-conditioning of the inverse moment problem (κ_n ~ 32^n), (II) complexity-theoretic reduction to Hamiltonian learning, and (III) physical irreversibility of scrambling dynamics (t_rec ~ 10^765). Hardness source I is unconditional and provides post-quantum security. Universality (Theorem 3): I establish the universality of the detection framework through systematic numerical verification across 8 Hamiltonian families and 10 perturbation types, achieving 8/8 families and 10/10 perturbation types at the physically relevant distance d = 1. All three results are detector-agnostic: they characterize the Krylov framework itself, independent of the specific detection algorithm applied to the Lanczos coefficients. Paper 9 in the Krylov QKD series. See also: qkd-krylov-detector on GitHub.
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.
Post-quantum cryptography currently rests on a small number of hardness assumptions, posing significant risks should any one of them be compromised. This vulnerability motivates the search for new and cryptographically versatile assumptions that make a convincing case for quantum hardness. In this work, we argue that decoding random quantum stabilizer codes---a quantum analog of the well-studied LPN problem---is an excellent candidate. This task occupies a unique middle ground: it is inherently native to quantum computation, yet admits an equivalent formulation with purely classical input and output, as recently shown by Khesin et al. (STOC '26). We prove that the average-case hardness of quantum stabilizer decoding implies the core primitives of classical Cryptomania, including public-key encryption (PKE) and oblivious transfer (OT), as well as one-way functions. Our constructions are moreover practically efficient: our PKE scheme achieves essentially the same efficiency as state-of-the-art LPN-based PKE. We also provide substantial evidence that stabilizer decoding does not reduce to LPN, suggesting that the former problem constitutes a genuinely new post-quantum assumption. Our primary technical contributions are twofold. First, we give a reduction from random quantum stabilizer decoding to an average-case problem closely resembling LPN, but which is equipped with additional symplectic algebraic structure. While this structure is essential to the quantum nature of the problem, it raises significant barriers to cryptographic security reductions. Second, we develop a new suite of scrambling techniques for such structured linear spaces, and use them to produce rigorous security proofs for all of our constructions.
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_{\mathrm{QBER}}(\tau )=\alpha (N)C_{\mathrm{op}}(\tau )CQBER​(τ)=α(N)Cop​(τ) C QBER ( τ ) = α ( N ) C op ( τ ) , with α(N)\alpha (N)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\mathrm{AUC}=0.9899AUC=0.9899 AUC = 0.9899 ). On 181,606181{,}606181,606 181 , 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%\Delta \mathrm{QBER}={+}0.5\%ΔQBER=+0.5% Δ QBER = + 0.5 % ( AUC=0.981\mathrm{AUC}=0.981AUC=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 paper investigates the emergence of the thermodynamic arrow of time in a closed 8-qubit quantum system. We analyze the tension between information scrambling and Poincaré recurrence by comparing two dynamical regimes: a near-integrable Heisenberg chain (Regime I) and a symmetry-broken chaotic regime (Regime II). Our central numerical result is a collapse of the Poincaré recurrence fidelity from F ≈ 0.99 to F ≈ 0.11 upon introducing symmetry-breaking fields. We provide structural analysis via Krylov subspace growth (Lanczos coefficients), illustrating that irreversibility in finite systems is an emergent property driven by spectral complexity. The global von Neumann entropy remains strictly zero in both regimes, confirming that information is conserved — the apparent irreversibility arises from the complexity of the path by which information returns, not from any fundamental loss. All results are obtained from exact unitary simulation of the Schrödinger equation; no Lindblad or Markov approximations are used. Simulation code: https://zenodo.org/records/18813710