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Physical Review A

Scintillation has minimal impact on far-field Bennett-Brassard 1984 protocol quantum key distribution

Jeffrey H. Shapiro

Published Sep 27, 2011• 22 citations
Publisher

Abstract

The effect of scintillation, arising from propagation through atmospheric turbulence, on the sift and error probabilities of a quantum key distribution (QKD) system that uses the weak-laser-pulse version of the Bennett-Brassard 1984 (BB84) protocol is evaluated. Two earth-space scenarios are examined: satellite-to-ground and ground-to-satellite transmission. Both lie in the far-field power-transfer regime. This work complements previous analysis of turbulence effects in near-field terrestrial BB84 QKD [J. H. Shapiro, Phys. Rev. A 67, 022309 (2003)]. More importantly, it shows that scintillation has virtually no impact on the sift and error probabilities in earth-space BB84 QKD, something that has been implicitly assumed in prior analyses for that application. This result contrasts rather sharply with what is known for high-speed laser communications over such paths, in which deep, long-lived scintillation fades present a major challenge to high-reliability operation.

DOI
10.1103/physreva.84.032340

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The effect of scintillation, arising from propagation through atmospheric turbulence, on the sift and error probabilities of a quantum key distribution (QKD) system that uses the weak-laser-pulse version of the Bennett-Brassard 1984 (BB84) protocol is evaluated. Two earth-space scenarios are examined: satellite-to-ground and ground-to-satellite transmission. Both lie in the far-field power-transfer regime. This work complements previous analysis of turbulence effects in near-field terrestrial BB84 QKD [J. H. Shapiro, Phys. Rev. A 67, 022309 (2003)]. More importantly, it shows that scintillation has virtually no impact on the sift and error probabilities in earth-space BB84 QKD, something that has been implicitly assumed in prior analyses for that application. This result contrasts rather sharply with what is known for high-speed laser communications over such paths, in which deep, long-lived scintillation fades present a major challenge to high-reliability operation.
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.
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.
Quantum key distribution (QKD) using free space optical (FSO) systems will, in most applications, involve atmospheric propagation. As is well known from classical FSO communication links, turbulence can cause large power variation in the link strength. Optical scintillation can cause fades below and surges above the mean power that last tens of milliseconds. Fades can be as deep as 20-30 dB. Previously we have demonstrated a system that allows laboratory studies of the effects of scintillation that faithfully represent the effects seen in the field. Scintillation is recorded using a modified FSO system and then played back in the laboratory using a fiber optic based system. The result is a laboratory experiment that reproduces, with high fidelity, the field conditions and component performance of the actual link. We have applied this same technique to studying scintillation effects on a QKD link. Scintillation was recorded at the US Naval Research Laboratory’s Maritime Lasercom Testbed This facility has sites on both sides of Chesapeake Bay separated by 16 km. A single-photon scintillation playback system was constructed. This scintillation playback system was designed to implement a BB84 protocol, but other QKD protocols could also be used. After the playback experiment the data can be analyzed to determine key length, error rate and other parameters. The set up can be used to study a variety of protocols for QKD in scintillation. Application to studies such as this will be presented.
There are numerous studies on the effects of ocean turbulence on wireless optical communications and on satellite–ground quantum key distribution (QKD); however, there are few studies on the impact of near sea-surface turbulence on ship-based QKD performance. This study investigates the influence of sea-surface atmospheric turbulence on laser beam propagation, atmospheric scintillation, and aiming error. It focuses on the impact of sea-surface turbulence on the performance of satellite-to-ship QKD and ship-to-ship QKD systems. The results show that strong turbulence severely degrades QKD system performance; horizontal transmission distances change from 32 km (weak turbulence) to 3 km (strong turbulence) in ship-to-ship QKD.
Satellite-based quantum key distribution (QKD) offers a pathway to secure global communications, yet its performance is fundamentally constrained by atmospheric turbulence. This paper presents a detailed analysis of the BBM92 entanglement-based protocol under realistic satellite-to-ground conditions using the Hufnagel-Valley turbulence model. We examine the role of key atmospheric factors, including wind speed, ground station altitude, and diurnal variations, on quantum performance metrics across a mean photon number (MPN) range of 0.001-0.3. Results reveal that turbulence strength, captured via the refractive index structure constant, governs channel transmittance through Rytov variance and scintillation index, directly impacting quantum bit error rate (QBER) and secret key rate (SKR). Simulations show that elevated ground stations improve SKR by15−25%1 5 - 2 5 \%15−25%, nighttime operation yields40 - 80 %\text{40 - 80 \%}40 - 80 %gains compared with daytime, and wind speeds of30m/s30 \mathrm{m} / \mathrm{s}30m/scan reduce SKR by up to 60% relative to10m/s10 \mathrm{m} / \mathrm{s}10m/sconditions. Optimal operation lies in the MPN range of 0.1-0.2, beyond which multiphoton noise degrades security as QBER approaches the 9% threshold.