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Optics Express

Security of AUV-carried OIRS-assisted quantum key distribution links in underwater channels subject to misalignment

Weina Pang, Ping Wang, Bo Bai, Wenwen Chen, Shuang Li, Kaile Wang

Published Jan 21, 2025• 2 citations
Publisher

Abstract

To establish a secure and high-bandwidth communication link between the gateway node and the central node in the internet of underwater things (IoUwT), it is meaningful to introduce quantum key distribution (QKD) protocols into underwater wireless optical communication (UWOC) systems. However, the line-of-sight (LOS) requirement for photon transmission will pose an inevitable challenge to the QKD-based UWOC system. In this work, an optical intelligent reflecting surface (OIRS) array mounted on an autonomous underwater vehicle (AUV) is utilized for the first time to alleviate the LOS blockage and enable more reliable underwater wireless optical quantum link for both discrete-variable quantum key distribution (DV-QKD) and continuous-variable quantum key distribution (CV-QKD). To begin with, a novel statistical model of the aggregated channel transmissivity experienced by the OIRS-based quantum states in underwater link is derived by combing the effects of oceanic absorption, scattering, turbulence and OIRS misalignment, where the oceanic turbulence-induced irradiance fluctuation is modeled by exponential and generalized gamma (EGG) distribution, and the jitter angle associated with AUV-carried OIRS misalignment is characterized by a Rayleigh distribution. Then, on the basis of this statistical model and the Gauss-Chebyshev quadrature, the quantum bit error rate and the lower bound secret key rate (SKR) for the AUV-carried OIRS-assisted DV-QKD link are obtained with weak coherent optical source and decoy state idea by utilizing Gottesman-Lo-Lütkenhaus-Preskill. In terms of univariate Fox-H function, the average Pirandola-Laurenza-Ottaviani-Banchi (PLOB) bound over the bosonic pure-loss channel, as well as the thermal upper and lower bounds over the thermal-loss channel are both derived for the AUV-carried OIRS-assisted CV-QKD link. Additionally, the achievable SKR for a practical GG02 CV-QKD protocol in underwater channels is also presented through the worst-case analysis. Furthermore, the impacts of the number of OIRS elements, OIRS positioning, jitter variances, the probability of erroneous detection and link distance on the security performance of the proposed links are studied with different water types, thereby offering valuable insights for the QKD-based UWOC system in IoUwT.

DOI
10.1364/oe.545449

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To establish a secure and high-bandwidth communication link between the gateway node and the central node in the internet of underwater things (IoUwT), it is meaningful to introduce quantum key distribution (QKD) protocols into underwater wireless optical communication (UWOC) systems. However, the line-of-sight (LOS) requirement for photon transmission will pose an inevitable challenge to the QKD-based UWOC system. In this work, an optical intelligent reflecting surface (OIRS) array mounted on an autonomous underwater vehicle (AUV) is utilized for the first time to alleviate the LOS blockage and enable more reliable underwater wireless optical quantum link for both discrete-variable quantum key distribution (DV-QKD) and continuous-variable quantum key distribution (CV-QKD). To begin with, a novel statistical model of the aggregated channel transmissivity experienced by the OIRS-based quantum states in underwater link is derived by combing the effects of oceanic absorption, scattering, turbulence and OIRS misalignment, where the oceanic turbulence-induced irradiance fluctuation is modeled by exponential and generalized gamma (EGG) distribution, and the jitter angle associated with AUV-carried OIRS misalignment is characterized by a Rayleigh distribution. Then, on the basis of this statistical model and the Gauss-Chebyshev quadrature, the quantum bit error rate and the lower bound secret key rate (SKR) for the AUV-carried OIRS-assisted DV-QKD link are obtained with weak coherent optical source and decoy state idea by utilizing Gottesman-Lo-Lütkenhaus-Preskill. In terms of univariate Fox-H function, the average Pirandola-Laurenza-Ottaviani-Banchi (PLOB) bound over the bosonic pure-loss channel, as well as the thermal upper and lower bounds over the thermal-loss channel are both derived for the AUV-carried OIRS-assisted CV-QKD link. Additionally, the achievable SKR for a practical GG02 CV-QKD protocol in underwater channels is also presented through the worst-case analysis. Furthermore, the impacts of the number of OIRS elements, OIRS positioning, jitter variances, the probability of erroneous detection and link distance on the security performance of the proposed links are studied with different water types, thereby offering valuable insights for the QKD-based UWOC system in IoUwT.
This paper studies intelligent reflecting surface (IRS)-assisted free space optical (FSO) quantum communication systems. An IRS can relax the requirement of a line-of-sight (LoS) link between Alice and Bob for FSO quantum key distribution (QKD) applications. The IRS focuses the laser beam toward Bob by introducing a phase shift to the incoming incident beam from Alice. Both discrete variable QKD (DV-QKD) and continuous variable QKD (CV-QKD) protocols for IRS-assisted QKD systems are studied. For DV-QKD, we characterize the average quantum bit error rate (QBER) and the achievable secret key rate (SKR) under a log-normal fading turbulence model. For CV-QKD, we present the ultimate quantum information-theoretic bounds for the SKR and entanglement distribution rates. We also characterize the achievable SKR of a practical CV-QKD protocol implemented using Gaussian coherent states. Our results reveal that Alice and Bob can generate a quantum secure key even if the LoS link between them is blocked by utilizing the IRS. Furthermore, with a quadratic phase shift profile, the IRS-assisted link achieves a higher SKR as compared to the direct LoS link and a relay-assisted link for large transmission distances.
Considering the ocean water’s optical attenuation and the roughness of the sea surface, we analyze the security of continuous-variable (CV) quantum key distribution (QKD) based air-to-water channel. The effects of the absorption and scattering on the transmittance of underwater quantum channel and the maximum secure transmission distance are studied. Considering the roughness of the sea surface, we simulate the performance bounds of CV QKD with different wind speeds using the Monte Carlo method. The results show that even if the secret key rate gradually reduces as the wind speed increases, the maximum transmission distance will not be affected obviously. Compared to the works regarding short-distance underwater optical communication, our research represents a significant step towards establishing secure communication between air platform and submarine vehicle .
Although underwater wireless optical communication (UWOC) receives much interest lately, security issues associated with it get little attention. In this work, it is the first attempt to investigate the physical layer security (PLS) performance of the vertical UWOC system with perfect and imperfect channel state information (CSI). Specifically speaking, the communication between two legitimate peers in the presence of an external eavesdropper is studied from the information-theoretic security perspective. Assuming that turbulence-induced fading over the vertical UWOC links is respectively subject to cascaded lognormal (LN) and Gamma-Gamma (GG) distributions for weak and moderate/strong turbulence conditions, and the angular pointing error is randomized by the Beckmann distribution, the composite cascaded statistical fading models are derived with the comprehensive effects of path loss, underwater turbulence, angular pointing errors, and channel estimation error. On the basis of these models, analysis frameworks of the probability of strictly positive secrecy capacity (SPSC), secrecy outage probability (SOP), and average secrecy capacity (ASC) are further obtained for this UWOC system, which are confirmed by Monte Carlo (MC) simulations. Furthermore, the effects including the number of layers, the level of channel estimation error, the link distance, the location of the eavesdropper, the quality of the main and eavesdropping channels on this system are analyzed for different water conditions. The presented results give valuable insights into the practical aspects of deployment of UWOC networks.
We experimentally demonstrated the feasibility of an underwater continuous-variable quantum key distribution (CV-QKD) system based on four-state protocol, which is promising to guarantee the unconditionally secure underwater wireless optical communication. CV-QKD parameter estimation is performed after transmitting quantum coherent signal from Alice to Bob through a water tank. The secure key rate under collective attack of the demonstrated CV-QKD system is estimated as 22.9 kbits/s at a channel loss of 12.4 dB. In addition, the performance is also investigated with various water types and the maximum underwater transmission distance of the demonstrated CV-QKD system is estimated as 148.7 m in the pure sea water.
The current literature on quantum key distribution (QKD) is mainly limited to the transmissions over fiber optic, atmospheric or satellite links and are not directly applicable to underwater environments with different channel characteristics. Absorption, scattering, and turbulence experienced in underwater channels severely limit the range of quantum communication links. In the first part of this thesis, we analyze the quantum bit error rate (QBER) and secret key rate (SKR) performance of the well-known BB84 protocol in underwater channels. As path loss model, we consider a modified version of Beer-Lambert formula which takes into account the effect of scattering. We derive a closed-form expression for the wave structure function to determine the average power transfer over turbulent underwater path and use this to obtain an upper bound on QBER as well as a lower bound on SKR. In the second part of this thesis, as a potential solution to overcome range limitations, we investigate a multi-hop underwater QKD where intermediate nodes between the source and destination nodes help the key distribution. We consider the deployment of passive relays which simply redirect the qubits to the next relay node or the receiver without any measurement. Based on the near-field analysis, we present the performance of relay-assisted QKD scheme in terms of QBER and SKR in different water types and turbulence conditions. In the last part of this thesis, we investigate the fundamental performance limits of decoy BB84 protocol over turbulent underwater channels and provide a comprehensive performance characterization. Based on near field analysis, we utilize the wave structure function to determine the average power transfer over turbulent underwater path and use this to obtain a lower bound on key generation rate. Based on this bound, we present the performance of decoy BB84 protocol in different water type.
We present a theoretical framework for quantum key distribution (QKD) using orbital angular momentum (OAM) encoded BB84 on an unmanned aerial vehicle (UAV) platform. A unified channel model captures Kolmogorov turbulence, pointing induced misalignment, and finite aperture clipping, enabling quantitative predictions of inter mode crosstalk and the resulting quantum bit error rate (QBER). Using a weak plus vacuum decoy state formulation, we derive composable finite key lower bounds on the secret key rate that incorporate statistical fluctuations, detector dark counts, efficiency mismatch, and error correction leakage. To stabilize performance under non stationary flight conditions, we introduce a lightweight physics informed learning module that combines physical priors with measured link statistics to classify valid pulses, reject corrupted data, and recommend decoding strategies. We outline a complete evaluation pipeline including UAV system architecture, turbulence driven QBER maps, decoy optimization, finite key scaling, and AI calibration metrics. Simulations indicate that under moderate turbulence and milliradian level pointing jitter, the proposed AI assisted method can improve the secret key rate by 10 percent to 30 percent while preserving composable security.