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Advanced Quantum Technologies

Impact of Atmospheric Turbulence on Spatial Mode Mismatch Attacks in Free‐Space QKD Implementation

Rachita Nandan, Tanya Sharma, R. P. Singh, Shashi Prabhakar

Published Dec 30, 2025• 0 citations
Publisher

Abstract

ABSTRACT In free‐space quantum key distribution (QKD), atmospheric turbulence affects quantum signals by causing intensity fluctuations, phase distortions, and beam wander, which may be exploited by an eavesdropper. Accurate characterization of the quantum channel and receiver is, therefore, essential. Detector efficiency mismatch has previously been identified as a possible side‐channel vulnerability. This study examines the impact of atmospheric turbulence on the security of a BB84 QKD receiver under a spatial‐mode mismatch attack. Turbulence is emulated in the laboratory using phase screens implemented on a spatial light modulator. Results show that turbulence exacerbates inherent detection probability mismatches, increasing the receiver's vulnerability. Information leakage to an eavesdropper is characterized and quantified based on both detection mismatches and turbulence strengths. A comparative analysis between Gaussian and Laguerre‐Gaussian (LG) modes shows that LG modes, particularly those of higher order, exhibit enhanced resilience against turbulence‐induced information leakage. These findings highlight the importance of receiver characterization and spatial mode selection for the secure implementation of QKD in long‐distance and satellite‐based systems under realistic atmospheric conditions.

DOI
10.1002/qute.202500460

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ABSTRACT In free‐space quantum key distribution (QKD), atmospheric turbulence affects quantum signals by causing intensity fluctuations, phase distortions, and beam wander, which may be exploited by an eavesdropper. Accurate characterization of the quantum channel and receiver is, therefore, essential. Detector efficiency mismatch has previously been identified as a possible side‐channel vulnerability. This study examines the impact of atmospheric turbulence on the security of a BB84 QKD receiver under a spatial‐mode mismatch attack. Turbulence is emulated in the laboratory using phase screens implemented on a spatial light modulator. Results show that turbulence exacerbates inherent detection probability mismatches, increasing the receiver's vulnerability. Information leakage to an eavesdropper is characterized and quantified based on both detection mismatches and turbulence strengths. A comparative analysis between Gaussian and Laguerre‐Gaussian (LG) modes shows that LG modes, particularly those of higher order, exhibit enhanced resilience against turbulence‐induced information leakage. These findings highlight the importance of receiver characterization and spatial mode selection for the secure implementation of QKD in long‐distance and satellite‐based systems under realistic atmospheric conditions.
The ability of an eavesdropper (Eve) to perform an intercept-resend attack on a free-space quantum-key-distribution (QKD) receiver by precisely controlling the incidence angle of an attack laser has been previously demonstrated. However, such an attack could be ineffective in the presence of atmospheric turbulence due to beam wander and spatial mode aberrations induced by the air's varying index of refraction. We experimentally investigate the impact turbulence has on Eve's attack on a free-space polarization-encoding QKD receiver by emulating atmospheric turbulence with a spatial light modulator. Our results identify how well Eve would need to compensate for turbulence to perform a successful attack by either reducing her distance to the receiver or using beam wavefront correction via adaptive optics. Furthermore, we use an entanglement-breaking scheme to find a theoretical limit on the turbulence strength that hinders Eve's attack.
Quantum key distribution (QKD) provides information-theoretic security and satellite-based quantum key distribution (SatQKD) has demonstrated the potential to extend this communication security to intercontinental scales. However, atmospheric turbulence induces significant distortion in the spatial distribution of received optical beams, while background noise remains approximately uniform across the detector plane. As a result, single-element qubit (quantum bit) detection can be frequently dominated by noise due to the random spatial pattern of the imaged wavefront, thereby degrading the system performance. To address this limitation, we propose to exploit the spatial degrees of freedom of single-photon detector arrays to reject the excessive noise while adapting to channel variations induced by turbulence. We develop a threshold-based selection method that only activates detector elements that have higher probability of registering qubits. We evaluate the performance of the proposed noise-rejection QKD schemes using Monte Carlo simulations considering the impact of diffraction and atmospheric turbulence on the transmitted optical beam in the presence of background and dark noise. The results show that, compared to conventional schemes, the proposed noise-rejection strategy effectively reduces the quantum bit error rate (QBER) and improves the secret key rate (SKR) performance, while the performance gains depend on the turbulence condition. These findings demonstrate the potential of adaptive array receiver design to enhance the robustness of the SatQKD system under realistic atmospheric conditions.
This paper explores the secrecy performance of the recently proposed intensity modulation/direct detection (IM/DD) terrestrial free-space quantum key distribution (QKD) system, by using a Gaussian-beam propagation model and considering the combined effects of atmospheric turbulence and legitimate transceivers’ misalignment. Secrecy performance metrics including quantum bit error rate (QBER) and ergodic secret-key rate are newly derived in closedform expressions, taking into account all combined effects of turbulence- and misalignment-induced fading channels, the eavesdropper’s location relative to the legitimate receiver, and receiver noises. To satisfy security constraints, the system designs based on the intensity modulation depth and beam waist of the Gaussian beam at the transmitter, and dualthreshold (D-T) selection at the receiver, are comprehensively discussed under turbulence and misalignment conditions as well as different eavesdropper’s locations. Monte-Carlo (M-C) simulations are also implemented to verify the analytical results. Remarkably, this paper also offers the first framework in the literature to evaluate the secrecy performance of free-space optical (FSO) systems considering the eavesdropper’s location under the effect of misalignment between legitimate transceivers.
Practical implementations of QKD protocols involve devices which are not perfect, and an eavesdropper may exploit this to gain information leading to attacks. Here we have considered the effects of coupling mismatch between the detectors. We find possible information leakage to Eve due to coupling mismatch at the receiver’s detectors in terms of mutual information between the eavesdropper and receiver. The experiment has been performed for the Gaussian and Laguerre-Gaussian modes of the signal. This aspect becomes essential while implementing free space QKD using a satellite. The results suggest that accounting for detection coupling mismatch is crucial to avoid side-channel attacks.
Abstract Quantum Key Distribution (QKD) provides information-theoretic security for future communication networks by exploiting the fundamental principles of quantum mechanics. However, satellite-to-ground QKD links suffer significant performance degradation due to atmospheric turbulence, absorption, scattering, and satellite-induced pointing errors. This paper investigates the BB84 QKD protocol over a Free-Space Optical (FSO) channel modeled using the Gamma–Gamma distribution, which accurately captures both small-scale and large-scale atmospheric irradiance fluctuations. Closed-form and numerical results for outage probability and Quantum Bit Error Rate (QBER) are presented under weak, moderate, and strong turbulence regimes. The Secure Key Rate (SKR) is analyzed as a function of link distance under clear and foggy weather conditions. Additionally, the impact of satellite vibration is evaluated using a jitter-dependent pointing error model, demonstrating that misalignment significantly reduces link reliability. Simulation results show that strong turbulence conditions introduce more than 15 dB SNR penalty compared to clear-sky operation, while haze conditions limit QKD range to under 8–10 km. These findings provide practical performance benchmarks for Low-Earth Orbit (LEO) quantum downlinks in realistic atmospheric environments. The results provide practical insights for electronic receiver design and system implementation of satellite quantum communication links.
Quantum Key Distribution (QKD) promises a provably secure method to transmit information from one party to another. Free-space QKD allows for this information to be sent over great distances and in places where fibre-based communications cannot be implemented, such as ground-satellite. The primary limiting factor for free-space links is the effect of atmospheric turbulence, which can result in significant error rates and increased losses in QKD channels. Here, we employ the use of a high-speed Adaptive Optics (AO) system to make real-time corrections to the wavefront distortions on spatial modes that are used for high-dimensional QKD in our turbulent channel. First, we demonstrate the effectiveness of the AO system in improving the coupling efficiency of a Gaussian mode that has propagated through turbulence. Through process tomography, we show that our system is capable of significantly reducing the crosstalk of spatial modes in the channel. Finally, we show that employing AO reduces the quantum dit error rate for a high-dimensional orbital angular momentum-based QKD protocol, allowing for secure communication in a channel where it would otherwise be impossible. These results are promising for establishing long-distance free-space QKD systems. High-dimensional quantum key distribution will allow for higher information density and greater error tolerance in future quantum networks. This work experimentally demonstrates how implementing an adaptive optics system in a spatial-mode free-space optical link can allow for quantum communications where it would otherwise be impossible.