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Topological Detection of Information Leakage in Open Quantum Channels: A Deterministic Framework via Nonlinear Dynamics

Rogerio Junior, Estevan Rychard

Published Apr 2, 2026• 0 citations
Publisher

Abstract

Quantum Key Distribution (QKD) provides unconditional security guaranteed by the laws of quantum mechanics. However, practical implementations remain vulnerable to physical-layer intrusions, such as the Photon-Number-Splitting (PNS) attack, which exploits non-ideal multi-photon emissions. Current countermeasures heavily rely on asymptotic statistical error bounds or complex optical hardware, introducing inherent detection latency. Building upon our foundational theoretical framework of fractal-entropic scaling, we introduce a protocol-agnostic, deterministic detection framework grounded in the dynamics of open quantum systems. We establish an operational isomorphism between the purity loss (ΔSL) induced by an eavesdropper and the topological symmetry breaking of nonlinear dynamic systems in the complex plane. By mapping discretized stochastic noise into a generalized complex iterative map, microscopic quantum perturbations are non-linearly amplified, forcing an orbital divergence in finite time. Hardware validation via fixed-point arithmetic on a Field-Programmable Gate Array (FPGA) demonstrates real-time, Layer-1 intrusion detection without relying on ideal quantum measurements. Using the BB84 protocol as a canonical case study, we prove that active quantum eavesdropping is topologically incompatible with the continuous natural noise of a secure channel.

DOI
10.5281/zenodo.19379211

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Quantum Key Distribution (QKD) provides unconditional security guaranteed by the laws of quantum mechanics. However, practical implementations remain vulnerable to physical-layer intrusions, such as the Photon-Number-Splitting (PNS) attack, which exploits non-ideal multi-photon emissions. Current countermeasures heavily rely on asymptotic statistical error bounds or complex optical hardware, introducing inherent detection latency. Building upon our foundational theoretical framework of fractal-entropic scaling, we introduce a protocol-agnostic, deterministic detection framework grounded in the dynamics of open quantum systems. We establish an operational isomorphism between the purity loss (ΔSL) induced by an eavesdropper and the topological symmetry breaking of nonlinear dynamic systems in the complex plane. By mapping discretized stochastic noise into a generalized complex iterative map, microscopic quantum perturbations are non-linearly amplified, forcing an orbital divergence in finite time. Hardware validation via fixed-point arithmetic on a Field-Programmable Gate Array (FPGA) demonstrates real-time, Layer-1 intrusion detection without relying on ideal quantum measurements. Using the BB84 protocol as a canonical case study, we prove that active quantum eavesdropping is topologically incompatible with the continuous natural noise of a secure channel.
Quantum Key Distribution (QKD) provides an innovative approach for secure communication by utilizing the principles of quantum mechanics. Among various QKD protocols, the BB84 protocol remains the most widely studied and implemented due to its simplicity and theoretical security guarantees. However, practical implementations of BB84 are vulnerable to several eavesdropping attacks and channel imperfections. This paper presents a comprehensive study on the detection and analysis of eavesdropping attacks in the BB84 protocol. The work focuses on common attacks such as intercept-resend attack, photon-number splitting attack, Trojan horse attack, and phase-covariant cloning attack. The effect of these attacks on Quantum Bit Error Rate (QBER) is analyzed in detail. Simulation-based observations are discussed to demonstrate how QBER increases under malicious interference. The study further explores statistical methods for detecting eavesdropping and examines practical countermeasures including decoy states, privacy amplification, and error correction techniques. The paper concludes that BB84 remains robust against eavesdropping when proper detection and mitigation mechanisms are employed.
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 is theoretically possible secure communication through the use of quantum-mechanical principles, such as superposition, measurement disturbance, and others. The BB84 and E91 protocols provide security by leveraging quantum principles against classical eavesdropping; nevertheless, the current implementation of QKD is vulnerable to photon-number-splitting attacks, imperfections in the devices used, and environmental quantum noise. Improving practical resistance to all of those is crucial for providing secure real-life use of QKD. Extending the current state-of-the-art through further development of research on eavesdropper detection and improvement of qubit-based security mechanisms, this research aims to develop the state-of-the art further by introducing a decoy-state BB84 framework and analyzing the behavior of such a system under realistic quantum noise. To find solutions to these problems, the current research will try to adopt the decoy-state BB84 model and analyze the system behavior under realistic quantum noise scenarios. So, the proposed approach, a standard BB84 protocol, will first be formulated and then further enhanced with decoy-state pulse generation to handle the vulnerabilities due to multi-photon pulses. Models like depolarizing noise, amplitude damping, and measurement errors will be used as real-world quantum channels. The model performance will be measured in terms of various performance metrics such as Key agreement ratio, Quantum Bit Error rate, and secure key rate for different qubit lengths. Scalability analysis and validation based on IBM quantum hardware will also be performed in order to measure the impact of real-world device noise on the reliability of generated keys.
Quantum Key Distribution (QKD) is one of the most promising technologies that enable theoretically unbreakable secure communications in this highly advanced information security era. This work provides a comparative analysis of QKD protocols such as BB84, Coherent One-Way (COW), and Differential Phase-Shift (DPS) against eavesdropping attacks e.g., Photon Number Splitting (PNS) attack. It employs a realistic approach to simulations such as using weak coherent pulse (WCP) sources. This work also explores qubit generation and the whole key distribution process in non-ideal conditions. Detailed algorithms have been discussed that simulate the encoding, transmission, and decoding process for every protocol, as well as simulating PNS attacks where an eavesdropper removes photons to gain key information without any detectable errors. Statistical metrics, such as Visibility and the information gain, are used to quantify the impact of these attacks. Future work aspects may include the extension of the simulation to incorporate additional parameters such as channel noise, fiber attenuation, detector dark counts, etc. to provide a realistic analysis to compare various QKD protocols.
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.
The practical implementation of Quantum Key Distribution (QKD) is heavily constrained by the PLOB bound [1], exponential optical channel loss, and device-dependent side-channel attacks [2]. We deductively elevate these limitations by structurally embedding the quantum optical channel into the 8-Dimensional Seonggil Matrix Space. By redefining decoherence and measurement disturbance as non-commutative quantum friction, the Topological Fractal Brake algebraically suppresses information leakage, bypassing classical linear bounds. This rigorously establishes a theoretical framework for a global, topologically lossless quantum internet without macroscopic repeater overhead.