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Six-State Quantum Key Distribution Eavesdropping Attacks as a Quantum Machine Learning Task

Sotel-Jackson, Jacob

Published Dec 5, 2025• 0 citations
Publisher

Abstract

Many modern classical encryption schemes, based on computational complexity, are threatened by quantum computers. Quantum Key Distribution (QKD) aims to address this threat, with security enforced by quantum-mechanical principles. The security of QKD protocols, like the six-state protocol (6QKD), relies on understanding all possible eavesdropping attacks. The optimal known individual eavesdropping attack on 6QKD in a noiseless channel is the Universal Quantum Cloning Machine (UQCM). However, the utility of quantum machine learning (QML) for QKD eavesdropping analysis is largely unexplored. The recent work by Decker et al. (2025) used QML to find new attacks on the four-state BB84 protocol, but this methodology has not yet been generalized to the more complex 6QKD protocol. This thesis generalizes the quantum circuit (QCL) learning framework to analyze individual eavesdropping attacks on 6QKD. We designed a parameterized quantum circuit (ansatz) appropriate for 6QKD, notably adapting our circuit to two ancilla, and expanding the measurement strategy to three bases. We used QCL to find the optimal attack parameters in a simulated noiseless, asymmetric (bit-flip, phase-flip), and symmetric (depolarizing) noise channels. In the noiseless quantum channel, the QCL successfully converges to and reproduces the theoretical performance of the UQCM, validating the adapted methodology. In the asymmetric bit-flip and phase-flip noise channels, the QCL discovers a novel "imbalanced cloner" attack that outperforms the standard UQCM in average fidelity. The model learns to exploit the noise asymmetry by sacrificing the fidelity in the degraded bases and gaining higher fidelity in the unaffected basis. In a symmetric depolarizing noise channel, the QCL performance converges exactly to the UQCM, demonstrating it finds no exploitable noise asymmetry. This work provides the first QCL-based security analysis of the 6QKD protocol. We demonstrate that the QCL is a generalizable tool for quantum security analysis. Furthermore, we present the first (to our knowledge) evidence of a 6QKD "imbalanced cloner" that outperforms UQCM in asymmetric noisy environments.

DOI
10.25394/pgs.30810293

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The rapid development of quantum computing threatens the traditional cryptographic schemes and suggests that the best alternative solution for ensuring the security of key exchange is Quantum Key Distribution (QKD).Despite the information-theoretic security guarantee, the practical implementations of QKD present vulnerabilities that were derived from hardware flaws and the exploitation of the quantum channel.This thesis is intended to address security vulnerabilities by analyzing and proposing an innovative architecture for the identification and mitigation of quantum attacks, via classification techniques of Quantum Machine Learning and the use of the metrics of Quantitative Risk Analysis.The study begins with the concepts of quantum information, the functionality of basic QKD protocols (BB84, B92, E91) and the mathematical modeling of Implementation-level attacks and side-channel attacks in quantum systems.Subsequently, the operational processes of Quantum Support Vector Machine (QSVM) and the Variational Quantum Classifier (VQC) are analyzed during the training phase.Based on the theoretical background of this study, QML-IDPS architecture is proposed.Threat detection and classification are performed using the QSVM and VQC classifiers, while risk metrics are utilized and fed into a classical Intrusion Prevention System (IPS) to support the final decision-making process for the prevention of quantum threats.The final key validated by the threat assessment mechanisms, is then used for data encryption with a classical cryptographic algorithm, such as AES-256.The proper functionality of QML-IDPS architecture is verified with the mathematical Intercept-Resend Use Case Scenario, which basically proves the successful classification and prevention of system anomalies.In conclusion, it is confirmed that the proposed QML-IDPS architecture demonstrates that Quantum Machine Learning combined with Quantitative Risk Analysis can enhance the security and reliability of QKD infrastructures.

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Many modern classical encryption schemes, based on computational complexity, are threatened by quantum computers. Quantum Key Distribution (QKD) aims to address this threat, with security enforced by quantum-mechanical principles. The security of QKD protocols, like the six-state protocol (6QKD), relies on understanding all possible eavesdropping attacks. The optimal known individual eavesdropping attack on 6QKD in a noiseless channel is the Universal Quantum Cloning Machine (UQCM). However, the utility of quantum machine learning (QML) for QKD eavesdropping analysis is largely unexplored. The recent work by Decker et al. (2025) used QML to find new attacks on the four-state BB84 protocol, but this methodology has not yet been generalized to the more complex 6QKD protocol. This thesis generalizes the quantum circuit (QCL) learning framework to analyze individual eavesdropping attacks on 6QKD. We designed a parameterized quantum circuit (ansatz) appropriate for 6QKD, notably adapting our circuit to two ancilla, and expanding the measurement strategy to three bases. We used QCL to find the optimal attack parameters in a simulated noiseless, asymmetric (bit-flip, phase-flip), and symmetric (depolarizing) noise channels. In the noiseless quantum channel, the QCL successfully converges to and reproduces the theoretical performance of the UQCM, validating the adapted methodology. In the asymmetric bit-flip and phase-flip noise channels, the QCL discovers a novel "imbalanced cloner" attack that outperforms the standard UQCM in average fidelity. The model learns to exploit the noise asymmetry by sacrificing the fidelity in the degraded bases and gaining higher fidelity in the unaffected basis. In a symmetric depolarizing noise channel, the QCL performance converges exactly to the UQCM, demonstrating it finds no exploitable noise asymmetry. This work provides the first QCL-based security analysis of the 6QKD protocol. We demonstrate that the QCL is a generalizable tool for quantum security analysis. Furthermore, we present the first (to our knowledge) evidence of a 6QKD "imbalanced cloner" that outperforms UQCM in asymmetric noisy environments.
We propose considering Quantum Key Distribution (QKD) protocols as a use case for Quantum Machine Learning (QML) algorithms. We define and investigate the QML task of optimizing eavesdropping attacks on the quantum circuit implementation of the BB84 protocol. QKD protocols are well understood and solid security proofs exist enabling an easy evaluation of the QML model performance. The power of easy-to-implement QML techniques is shown by finding the explicit circuit for optimal individual attacks in a noise-free setting. For the noisy setting we find, to the best of our knowledge, a new cloning algorithm, which can outperform known cloning methods. Finally, we present a QML construction of a collective attack by using classical information from QKD post-processing within the QML algorithm.
Quantum key distribution (QKD) links are provisioned from security analyses of stationary channels, whereas the devices that determine the channel drift between recalibrations. Whether an eavesdropper who cannot alter the channel's own noise gains by following that drift has not been quantified. Adaptive eavesdropping is posed here as a constrained Markov decision process in which the attacker selects one circuit per round while the noise level follows an Ornstein--Uhlenbeck process and the abort condition is a budget over each block of rounds. The value of adaptation is bounded by the best fixed circuit and a dynamic-programming upper bound. The actions are learnt attacks. Whereas Decker et al. trained a parametrised circuit on a fixed gate template against a fixed channel, here the gate structure and rotation angles are searched jointly. This yields circuits compact enough to form a discrete action set, extending the construction to noise models lacking a known template, including the amplitude damping channel. On device-independent E91 under bilateral depolarising noise, a reinforcement-learning attacker raises her Holevo information from 0.1350.1350.135 for the best fixed circuit to 0.3480.3480.348 at zero detection, 98%98\%98% of the upper bound. On BB84 under a drifting bit-flip channel, she exceeds a conservative noise-indexed rule by 0.0240.0240.024 in fidelity, reaching 99%99\%99% of the upper bound. Under stationary noise, the attacker's gain from basis asymmetry changes sign between an averaged and a per-basis error-rate constraint. The search, started from random gate sequences, recovers the analytical cloners and the collective-attack key rate, and meets the lower bound of the Winick--Lütkenhaus--Coles objective from above.
We investigate the connection between the optimal collective eavesdropping attack and the optimal cloning attack where the eavesdropper employs an optimal cloner to attack the quantum key distribution (QKD) protocol. The analysis is done in the context of the security proof in Refs. [Proc. R. Soc. London A 461, 207 (2005); Phys. Rev. Lett. 95, 080501 (2005)] for discrete variable protocols in ddd-dimensional Hilbert spaces. We consider a scenario in which the protocols and cloners are equipped with symmetries. These symmetries are used to define a quantum cloning scenario. We find that, in general, it does not hold that the optimal attack is an optimal cloner. However, there are classes of protocols, where we can identify an optimal attack by an optimal cloner. We analyze protocols with 2, ddd and d+1d+1d+1 mutually unbiased bases where ddd is a prime, and show that for the protocols with 2 and d+1d+1d+1 mutually unbiased bases (MUBs) the optimal attack is an optimal cloner but, for the protocols with ddd MUBs, it is not. Finally, we give criteria to identify protocols which have different signal states, but the same optimal attack. Using these criteria, we present qubit protocols which have the same optimal attack as the Bennett-Brassard 1984 (BB84) protocol or the 6-state protocol.
Quantum key distribution (QKD) is widely regarded as a highly secure quantum encryption approach since it applies theoretical principles of quantum mechanics as a medium of security, unlike classical encryption processes that rely on complex mathematics. However, practical QKD systems are vulnerable due to imperfect photon source hardware, communication channel, and detector implementation. These hardware imperfections open side channels that an adversary can exploit without violating principles of quantum mechanics. This review provides a comprehensive overview of the current QKD protocols, quantum hacking strategies and their operating principles, vulnerable hardware components and their mitigation techniques. This paper further investigates how state-of-the-art paradigms based on artificial intelligence (AI) and machine learning (ML), along with key subfields—such as deep learning (DL), deep reinforcement learning (DRL), and quantum machine learning (QML)—are reshaping the domain. In particular, this paper analyzes their dual roles as enablers of sophisticated attacks and as instruments for attack detection and mitigation. By jointly addressing the challenges in quantum communication and adaptive learning, as well as attack and detection architectures, this survey elucidates both the capabilities and the limitations of contemporary attack-detection mechanisms in the field. This survey seeks to establish a unified framework that conceptually integrates physical-layer quantum hacking with AI-/ML-based security, emphasizing their dual function as both an intelligent defensive layer and a potential tool for advanced threats.
In this thesis we develop practical tools for quantum key distribution (QKD) security proofs. We apply the tools to provide security proofs for several protocols, ranging from discrete variable protocols in high dimensions, protocols with realistic implementations, measurement device independent QKD and continuous-variable QKD. The security proofs are based on the Devetak-Winter security framework [I. Devetak and A. Winter, Proc. of the Roy. Soc. of London Series A, 461, 207 (2005); B. Kraus, N. Gisin, and R. Renner, Phys. Rev. Lett., 95 080501 (2005)]. \n \nIn the key rate calculation, it is often convenient to assume that the optimal attack is symmetric. \nUnder the assumption that the parameter estimation is based on coarse-grained observations, we show that the optimal attack is symmetric, if the protocol and the postselection have sufficient symmetries. \nAs an example we calculate the key rates of protocols using 2, d and d+1 mutually unbiased bases in d-dimensional Hilbert spaces. \n \nWe investigate the connection between the optimal collective eavesdropping attack and the optimal cloning attack, in which the eavesdropper employs an optimal cloner to attack the protocol. \nWe find that, in general, it does not hold that the optimal attack is an optimal cloner. However, there are classes of protocols, for which we can identify the optimal attack by an optimal cloner. \nWe analyze protocols with mutually unbiased bases in d dimensions, and show that for the protocols with 2 and d+1 mutually unbiased bases the optimal attack is an optimal cloner, but for the protocols with d mutually unbiased bases, it is not. \n \nIn optical implementations of the phase-encoded BB84 protocol, the bit information is usually encoded in the phase of two consecutive photon pulses generated in a Mach-Zehnder interferometer. In the actual experimental realization, the loss in the arms of the Mach-Zehnder interferometer is not balanced, for example because only one arm contains a lossy phase modulator. \nSince the imbalance changes the structure of the signals states and measurements, the BB84 security analysis no longer applies in this scenario. \nWe provide a security proof for the unbalanced phase-encoded BB84. The loss does lower the key rate compared to a protocol without loss. However, for a realistic parameter regime, the same key rate is found by applying the original BB84 security analysis. \n \nRecently, the security of a measurement device-independent QKD setup with BB84 signal states was proven in Refs. [H.-K. Lo, M. Curty, and B. Qi, Phys. Rev. Lett., 108 (2012); S. L. Braunstein and S. Pirandola, Phys. Rev. Lett., 108 (2012)]. In this setup Alice and Bob send quantum states to an intermediate node, which performs the measurement, and is assumed to be controlled by Eve. \nWe analyze the security of a measurement device-independent QKD protocol with B92 signal states, and calculate the key rates numerically for a realistic implementation. \nBased on our security proof we were able to prove the security of the strong reference pulse B92 protocol. \n \nWe analyze the security of continuous-variable protocols using the entropic uncertainty relations established in Ref. [M. Berta, M. Christandl, R. Colbeck, J. M. Renes, and R. Renner, Nature Physics 6, 659 (2010)] to provide an estimate of the key rate based on the observed first and second moments. We analyze a protocol with squeezed coherent states and the 2-state protocol with two coherent states with opposite phases.
The rapid development of quantum computing threatens the traditional cryptographic schemes and suggests that the best alternative solution for ensuring the security of key exchange is Quantum Key Distribution (QKD).Despite the information-theoretic security guarantee, the practical implementations of QKD present vulnerabilities that were derived from hardware flaws and the exploitation of the quantum channel.This thesis is intended to address security vulnerabilities by analyzing and proposing an innovative architecture for the identification and mitigation of quantum attacks, via classification techniques of Quantum Machine Learning and the use of the metrics of Quantitative Risk Analysis.The study begins with the concepts of quantum information, the functionality of basic QKD protocols (BB84, B92, E91) and the mathematical modeling of Implementation-level attacks and side-channel attacks in quantum systems.Subsequently, the operational processes of Quantum Support Vector Machine (QSVM) and the Variational Quantum Classifier (VQC) are analyzed during the training phase.Based on the theoretical background of this study, QML-IDPS architecture is proposed.Threat detection and classification are performed using the QSVM and VQC classifiers, while risk metrics are utilized and fed into a classical Intrusion Prevention System (IPS) to support the final decision-making process for the prevention of quantum threats.The final key validated by the threat assessment mechanisms, is then used for data encryption with a classical cryptographic algorithm, such as AES-256.The proper functionality of QML-IDPS architecture is verified with the mathematical Intercept-Resend Use Case Scenario, which basically proves the successful classification and prevention of system anomalies.In conclusion, it is confirmed that the proposed QML-IDPS architecture demonstrates that Quantum Machine Learning combined with Quantitative Risk Analysis can enhance the security and reliability of QKD infrastructures.