Nowadays, a high level of security is required for the transmission of critical information. Quantum Key Distribution (QKD) systems are considered the best option to protect such information. Many studies have shown the efficiency of the QKD optical fiber inspired by M-ary pulse position modulation (MPPM). Free-Space Optical (FSO) links provide an efficient and effective data transmission system. However, cumulative effects of laser beam divergence, misalignment, 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. This paper introduces the development of an FSO system based on the MPPM and the BB84 protocol (MPPM-BB84) over the Gamma-Gamma (GG) turbulence channel with pointing errors. Time Binning is implemented using MPPM to increase system security and reduce the quantum bit error rate (QBER). The system security is investigated under photon number splitting attack and excess noise. Closed-form expressions for asymptotic expressions of the average symbol error probability (SER), raw key rate (RKR), and secret key rate (SKR) are introduced. Moreover, the Monte-Carlo simulations are then used to prove the validity of the analytical results. The optimal values for the average photon number per pulse (to achieve the maximum RKR and SKR) for each symbol length can guarantee the stability of the FSO system under different weather conditions. Smaller symbol lengths are more tolerant of detector loss. The proposed system supports linking distances from 1 km to 3 km while keeping the SKR almost constant.
Nowadays, a high level of security is required for the transmission of critical information. Quantum Key Distribution (QKD) systems are considered the best option to protect such information. Many studies have shown the efficiency of the QKD optical fiber inspired by M-ary pulse position modulation (MPPM). Free-Space Optical (FSO) links provide an efficient and effective data transmission system. However, cumulative effects of laser beam divergence, misalignment, 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. This paper introduces the development of an FSO system based on the MPPM and the BB84 protocol (MPPM-BB84) over the Gamma-Gamma (GG) turbulence channel with pointing errors. Time Binning is implemented using MPPM to increase system security and reduce the quantum bit error rate (QBER). The system security is investigated under photon number splitting attack and excess noise. Closed-form expressions for asymptotic expressions of the average symbol error probability (SER), raw key rate (RKR), and secret key rate (SKR) are introduced. Moreover, the Monte-Carlo simulations are then used to prove the validity of the analytical results. The optimal values for the average photon number per pulse (to achieve the maximum RKR and SKR) for each symbol length can guarantee the stability of the FSO system under different weather conditions. Smaller symbol lengths are more tolerant of detector loss. The proposed system supports linking distances from 1 km to 3 km while keeping the SKR almost constant.
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.
Abstract In this paper, we analyze the performance of free-space optical quantum key distribution (FSO-QKD) using the BB84 protocol with BPSK modulation under realistic channel conditions. The Málaga distribution is employed to model the composite atmospheric turbulence, considering pointing errors. We derive closed-form expressions for the average quantum bit error rate (QBER) and the secure key rate (SKR), incorporating both turbulence and misalignment effects. Numerical results demonstrate the impact of turbulence parameters and beam misalignment on system performance. The findings provide insights for the robust design of FSO-QKD systems under practical deployment conditions.
We devoted to analyzing information transfer in quantum channels in terms of the performance of quantum key distribution (QKD) free-space optical (FSO) communication systems through Bennett and Brassard 84 (BB84) protocol by taking into account the combined effect of attenuation, turbulence, pointing error, and angle of arrival (AOA) fluctuations. Path loss is modeled by Beer-Lambert law, and the turbulent channel is assumed to be Fisher-Snedecor F distributed. The pointing error and AOA fluctuations are modeled by Hoyt and Rayleigh distributions, respectively. The error and sift probabilities, quantum bit error rate, and secret key rate of a QKD FSO system are obtained in analytical form, and results are presented depending on various parameters. It is shown that increased beam waist, beam deviation, AOA fluctuations, and propagation distance cause performance degradation and less secure information transmission. However, an increase in the ratio of horizontal and vertical beam misalignments, field of view, average photon number per pulse, visibility of the atmospheric environment, and optical beam wavelength impact the performance of QKD FSO systems positively. The effect of the turbulence structure constant is observed to be modest on the performance of the QKD FSO system.
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=10−3and threshold outage probability=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.
Quantum cryptography is a promising technology that achieves unconditional security, which is essential to a wide range of sensitive applications. In contrast to optical fiber, the free-space optical (FSO) link is efficiently used as a quantum channel without affecting the polarization of transmitted photons. However, the FSO link has several impairments, such as atmospheric turbulence and pointing errors, which affect the performance of the quantum channel. This paper proposes a quantum key distribution (QKD) scheme that uses a time-bin entanglement protocol over the FSO channel that suffers from various channel impairments. Due to the interest in unmanned aerial vehicles (UAVs) and their usefulness for many social, internet-of-things (IoT), civil, and military applications, the proposed QKD-FSO system is integrated with the ground-to-UAV platform. Furthermore, variances in the position and orientation of the UAV are investigated using a tracking system. These variances are considered when evaluating the overall performance of the proposed integrated system. For this purpose, closed-form expressions are obtained for the system average symbol error rate (ASER) and outage probability. The Monte Carlo simulation is used to verify the validity of the proposed expressions. The system security is investigated assuming photon number splitting (PNS) attack. Moreover, the transmit power, time-bin number, and modulation order are optimized to maximize the raw and secret key rates. The results show that for 500 m link, ASER22 mrad and signal-to-noise ratio > 7.5 dB which leads SNRth < 2.5 dB and raw key rate maximized by adjusting the number of time bins according to the received SNR.
Secure data transmission is essential in today's world, and quantum key distribution (QKD) is widely recognized as the technology of choice to enable information-theoretical secure symmetric key generation. While optical fibers are typically used as a transmission channel, wireless transmission offers the flexibility to reach every part of the Earth; moreover, for Earth-Satellite QKD, wireless communication naturally becomes a necessity. In this study, we deployed a fiber-wireless optical system that transmitted a 64-QAM 400 Gbps classical signal for high-rate data exchange and a 1 MHz quantum signal for QKD. The impact of turbulence in the quantum system is evaluated by transmitting single-polarization quantum states through a turbulent free-space channel and by calculating the respective intrinsic quantum bit error rate (QBER). From this, we estimate the system's secret key rate (SKR) and its dependence on turbulence. The effects of atmospheric turbulence on the optical wireless signal were emulated and investigated by using a custom-made atmospheric chamber to induce different turbulent scenarios. The atmospheric chamber allowed us to vary the turbulence in a Rytov variance range from 0.06 to 2.52. The classical signal showed an overall average reliability of 82% for the mentioned turbulence regimes. The results of the quantum signal showed that for Rytov variances up to 1.3, and under the conditions tested, secret key generation is possible, reaching a maximum SKR of 8.7×10−4bits per pulse during the produced turbulence regimes.