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Chinese Physics B

Analysis of atmospheric effects on the continuous variable quantum key distribution

Tao Liu, Shuo Zhao, Ivan B. Djordjević, Shuyu Liu, Sijia Wang, Tong S. Wu, Bin Li, Pingping Wang, Rongxiang Zhang

Published Apr 28, 2022• 1 citation
Publisher

Abstract

Atmospheric effects have significant influence on the performance of a free-space optical continuous variable quantum key distribution (CVQKD) system. In this paper, we investigate how the transmittance, excess noise and interruption probability caused by atmospheric effects affect the secret-key rate (SKR) of the CVQKD. Three signal wavelengths, two weather conditions, two detection schemes, and two types of attacks are considered in our investigation. An expression aims at calculating the interruption probability is proposed based on the Kolmogorov spectrum model. The results show that a signal using long working wavelength can propagate much further than that of using short wavelength. Moreover, as the wavelength increases, the influence of interruption probability on the SKR becomes more significant, especially within a certain transmission distance. Therefore, interruption probability must be considered for CVQKD by using long-signal wavelengths. Furthermore, different detection schemes used by the receiver will result in different transmission distances when subjected to individual attacks and collective attacks, respectively.

DOI
10.1088/1674-1056/ac6b1f

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Atmospheric effects have significant influence on the performance of a free-space optical continuous variable quantum key distribution (CVQKD) system. In this paper, we investigate how the transmittance, excess noise and interruption probability caused by atmospheric effects affect the secret-key rate (SKR) of the CVQKD. Three signal wavelengths, two weather conditions, two detection schemes, and two types of attacks are considered in our investigation. An expression aims at calculating the interruption probability is proposed based on the Kolmogorov spectrum model. The results show that a signal using long working wavelength can propagate much further than that of using short wavelength. Moreover, as the wavelength increases, the influence of interruption probability on the SKR becomes more significant, especially within a certain transmission distance. Therefore, interruption probability must be considered for CVQKD by using long-signal wavelengths. Furthermore, different detection schemes used by the receiver will result in different transmission distances when subjected to individual attacks and collective attacks, respectively.
Compared to fiber continuous-variable quantum key distribution (CVQKD), atmospheric link offers the possibility of a broader geographical coverage and more flexible transmission. However, there are many negative features of the atmospheric channel that will reduce the achievable secret key rate, such as beam extinction and a variety of turbulence effects. Here we show how these factors affect performance of CVQKD, by considering our newly derived key rate formulas for fading channels, which involves detection imperfections, thus form a transmission model for CVQKD. This model can help evaluate the feasibility of experiment scheme in practical applications. We found that performance deterioration of horizontal link within the boundary layer is primarily caused by transmittance fluctuations (including beam wandering, broadening, deformation, and scintillation), while transmittance change due to pulse broadening under weak turbulence is negligible. Besides, we also found that communication interruptions can also cause a perceptible key rate reduction when the transmission distance is longer, while phase excess noise due to arrival time fluctuations requires new compensation techniques to reduce it to a negligible level. Furthermore, it is found that performing homodyne detection enables longer transmission distances, whereas heterodyne allows higher achievable key rate over short distances.
In the free-space quantum communication, the performance of communication systems has a great degradation due to the atmospheric effects, such as atmospheric absorption, scattering and turbulence. However, quantum signals with different wavelengths is differently affected by atmospheric characteristics. In this paper, in order to investigate the effects of different wavelengths quantum signals on free-space quantum key distribution, an entanglement-based continuous variable quantum key distribution transmission model is established. Considering the influence of various atmospheric effects on quantum signals, the secret key generation rates are calculated though the homodyne detectors. The simulation results show that the long-wavelength signal can enhance the secret key generation rates at the same transmission distance. Therefore, the long-wavelength signal is more suitable for the free-space quantum transmission.
Compared with the fiber channel, the atmospheric channel offers the possibility of a broader geographical coverage and more flexible transmission for continuous-variable quantum key distribution (CVQKD). However, the fluctuation of atmospheric conditions will lead to the loss of performance in atmospheric quantum communication. In this paper, we study how temperature affects atmospheric CVQKD. We mainly consider the temperature effects on the transmittance and interruption probability. From the numerical simulation analysis, it can be shown that the performance of atmospheric CVQKD is improved as temperature increases, with the other factors fixed. Moreover, the results in this work can be used to evaluate the feasibility of the experimental implementation of the atmospheric CVQKD protocols.
Recently, several practical wavelength attacks on continuous-variable quantum key distribution (CVQKD) were proposed based on the wavelength-dependent property of a beam splitter in Bob's station. These attack schemes are limited to the fiber channel systems with a relatively stable transmittance. However, unlike the fiber channel, the transmittance of the atmospheric channel is complex and fluctuates dramatically in time, which may invalidate the attack equations that must be satisfied in the optical fiber channel. In this paper, we propose two wavelength attack schemes against complex atmospheric CVQKD systems and formulize the two schemes based on the parameter estimation method. To verify the feasibility and availability of this attack, we deduce the success criteria for the two attack schemes. By numerical analysis, our attack schemes are proved to be feasible in the permitted parameter regimes. The secret key rate and propagation distance of CVQKD can be further overestimated by selecting the condition parameters effectively. Moreover, we discuss the possible prevention countermeasures to resist these attack schemes. The proposed method will fill the gap of wavelength attack for the implementation of practical atmospheric CVQKD.
Continuous variable quantum key distribution (CVQKD) has been implemented over the atmospheric channels over free space. However, atmospheric turbulence weakens the quality of the transmitting quantum signals and hence decreases the secret key rate of the system. Here, we suggest an atmospheric turbulence channel model that involves atmospheric turbulence bubbles and demonstrates the implementation feasibility of passive CVQKD with spectrum resources in the terahertz band over the atmospheric turbulence channel. We achieve the channel transmittance characterized by the refractive index and the wavefront distortions. Moreover, an adaptive optics (AO) unit is used for performance improvement while considering the effect of the thermal noise and excess noise on the atmospheric turbulence bubble-modeled channel. Numerical simulations show that the AO-involved detection scheme can result in reductions in excess noise when being faced with the floating clouds and mist in atmospheric turbulence, which results in performance improvements in terms of secret key rate, which confirms the utility of the high-rate and long-distance CVQKD in terahertz (THz) for practical implementations.
Atmospheric effects are the chief threats to the quantum properties of propagating quantum signals and may degrade the performance of quantum key distribution seriously. As one of the most important parts of continuous-variable quantum key distribution (CVQKD), a parameter estimation method has not been specially proposed in an atmospheric channel, and usually the security analysis is based on the assumption that the relevant parameters, especially the excess noise, have been previously obtained. Here we propose a parameter estimation method for Gaussian modulated coherent state continuous-variable quantum key distribution over the atmospheric link, and we investigate the impact of the atmospheric channel on the estimated values of the parameters. Based on this method, we study theoretically the effect of link fluctuations on the achievable secret key rate of CVQKD under different practical transmitted conditions. The results show that this method is unified with the physical model and can effectively resist entanglement-distillation attack. The proposed method fills in the blank of parameter estimation for implementation of practical atmospheric CVQKD.