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Performance of DVQKD Protocol Over Gamma Gamma Turbulence Channel

Abhishek Mani Shukla, Neel Kanth Kundu

Published Jan 6, 2025• 1 citation
Publisher

Abstract

In this paper, we investigate the performance of a discrete variable quantum key distribution (DV-QKD) system over a turbulence channel under moderate to strong turbulence conditions. We employ the Gamma-Gamma turbulence model for the turbulence channel and derive analytical expressions for the average quantum bit error rate (QBER) and secrecy key rate (SKR) of the decoy state DV-QKD protocol. Both analytical and numerical simulation results demonstrate that, for the decoy-state QKD protocol, the QBER of the FSO system highly depends on the link length but is largely unaffected by turbulence strength. Furthermore, the numerical simulation results reveal that the SKR remains stable even under stronger turbulence.

DOI
10.1109/comsnets63942.2025.10885724

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Unmanned aerial vehicles (UAV) based on free-space optical (FSO) systems combine the benefits of both the high data rate of the FSO and the mobility of UAV. However, cumulative effects of laser beam divergence and turbulence-induced fading on the received irradiance in the FSO link might allow an external eavesdropper located near the authorized receiver to break the transmission under certain conditions. Quantum key distribution (QKD) is a technique of secure communication that employs quantum mechanics-based cryptography principles. A combination of a continuous-variable quantum key distribution (CV-QKD) and Gaussian modulation of quantum coherent states (GMCS) enables a relatively secure communication system against collective attacks over FSO transmission links. However, the performance is restricted and degraded due to the influence of atmospheric turbulence and excess noise. This paper aims to evaluate the performance of a secured UAV-based FSO system utilizing prepare and measure CV-QKD protocol based on GMCS under collective attack in terms of quantum bit error rate (QBER), outage probability, and secret key rate (SKR) considering the impairments of the FSO channel, link budget, deviations in the position and attitude angles of the UAV, channel fluctuating transmittance, and excess noise. The system parameters, including transmit power, receiver’s field-of-view, and beam divergence angle, are optimized to satisfy the system’s design criteria of threshold-QBER=10−3=10^{-3}=10−3and threshold outage probability=10−2=10^{-2}=10−2. The proposed system tolerates boresight displacement up to 7 cm with the optimized values. The Closed-form expressions and analytical results are confirmed by Monte-Carlo simulations.
The current literature on quantum key distribution is limited mainly to transmissions over fiber optic, atmospheric, or satellite links and is not directly applicable to underwater environments with different channel characteristics. In this paper, we analyze the quantum bit error rate (QBER) and secret key rate (SKR) performance of the well-known BB84 protocol in underwater channels. As a path loss model, we consider a modified version of the 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 a turbulent underwater path and use this to obtain an upper bound on QBER as well as a lower bound on SKR. Based on the derived bounds, we present the performance of the BB84 protocol in different water types including clear, coastal, and turbid and under different atmospheric conditions such as clear, hazy, and overcast. We further investigate the effect of system parameters such as aperture size and detector field of view on QBER and SKR performance metrics.
Abstract In Discrete Variable Quantum Key Distribution (DV-QKD), the homodyne detection method is frequently employed for its simplicity in use, effectiveness in terms of error correction, and suitability with contemporary optical communication systems. Being a coherent detection method, it relies on a local oscillator whose frequency is matched to that of the transmitted carrier's signal. In this paper, we evaluate a Free Space Optical (FSO) DV-QKD system based on the KMB09 protocol using Homodyne detection under random phase fluctuation and depolarizing noise error. We present simulation results for System Efficiency and Quantum Bit Error Rate (QBER) for the proposed model. An obtained efficiency ({25%25\%25%}) for our proposed DV-QKD system model shows that under atmospheric turbulence and noise effect and it is in line with the available analytical results. However, the inclusion of random phase fluctuation and noise led to higher-than-normal QBER which is anticipated in a real-world scenario.