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Applied Sciences

Monte Carlo-Based Performance Analysis for Underwater Continuous-Variable Quantum Key Distribution

Yiyu Mao, Xuelin Wu, Wenti Huang, Qin Liao, Han Wu Deng, Yijun Wang, Ying Guo

Published Aug 19, 2020• 26 citations
Publisher

Abstract

There is a growing interest in the security of underwater communication with the increasing demand for undersea exploration. In view of the complex composition and special optical properties of seawater, this paper deals with a performance analysis for continuous-variable quantum key distribution (CVQKD) over an underwater link. In particular, we focus on analyzing the channel transmittance and detection efficiency based on Monte Carlo simulation for different water types, link distances and transceiver parameters. A comparison between the transmittance obtained by simple Beer’s law and Monte Carlo simulation reveals that the transmittance of underwater link may be severely underestimated in the previous underwater CVQKD research. The effect of the receiver aperture and field of view (FOV) on detection efficiency under different water types is further evaluated based on Monte Carlo. Simulation results show that the transmission distance of the underwater CVQKD system obtained by Monte Carlo simulation in pure sea water, clear ocean water and coastal ocean water is larger than that obtained by Beer’s law, while the key rate of the system in all types of water is smaller than that obtained by Beer’s law because the size and FOV of the receiver aperture are taken into account. By considering the practical system parameters, this paper establishes a comprehensive model for evaluating the security of underwater CVQKD systems with different system configurations.

DOI
10.3390/app10175744

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There is a growing interest in the security of underwater communication with the increasing demand for undersea exploration. In view of the complex composition and special optical properties of seawater, this paper deals with a performance analysis for continuous-variable quantum key distribution (CVQKD) over an underwater link. In particular, we focus on analyzing the channel transmittance and detection efficiency based on Monte Carlo simulation for different water types, link distances and transceiver parameters. A comparison between the transmittance obtained by simple Beer’s law and Monte Carlo simulation reveals that the transmittance of underwater link may be severely underestimated in the previous underwater CVQKD research. The effect of the receiver aperture and field of view (FOV) on detection efficiency under different water types is further evaluated based on Monte Carlo. Simulation results show that the transmission distance of the underwater CVQKD system obtained by Monte Carlo simulation in pure sea water, clear ocean water and coastal ocean water is larger than that obtained by Beer’s law, while the key rate of the system in all types of water is smaller than that obtained by Beer’s law because the size and FOV of the receiver aperture are taken into account. By considering the practical system parameters, this paper establishes a comprehensive model for evaluating the security of underwater CVQKD systems with different system configurations.
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 .
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Continuous variable quantum key distribution (CVQKD) can be potentially implemented through seawater channels, whereas the involved oceanic turbulence has a negative effect on the maximal transmission distance of quantum communication systems. Here, we demonstrate the effects of the oceanic turbulence on the performance of the CVQKD system and suggest an implementation feasibility of the passive CVQKD through the oceanic turbulence-based channel. We achieve the channel transmittance characterized by the transmission distance and depth of the seawater. Moreover, a non-Gaussian approach is used for performance improvement while counteracting the effects of excess noises on the oceanic channel. Numerical simulations show that the photon operation (PO) unit can bring reductions of excess noise when taking into account the oceanic turbulence, and hence results in performance improvement in terms of transmission distance and depth as well. The passive CVQKD explores the intrinsic field fluctuations of a thermal source without using an active scheme and hence has a promising application in chip integration for portable quantum communications.
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.
Cross-media and confidentiality are key features of next-generation optical communications. Quantum communication is regarded as a promising new form of secure communication. However, the cross-media transmission of quantum pulses tends to suffer from severe attenuation, which inevitably degrades the security of the whole system. In this paper, we consider the configuration of the continuous-variable quantum key distribution through an air–water cross-media channel that involves the lower-atmospheric channel, the underwater channel, and the air–water interface. We consider the effect of air bubbles in seawater, and the effect of the dynamic air–water interface as well. In particular, dynamic characteristics of light extinction and fluctuations caused by seawater and bubbles have been demonstrated with Monte Carlo (MC) simulations. Based on this MC-based model, we demonstrate the communication viability, and simulation results show that in clear seawater conditions with a wind speed of 5 m/s and a zenith angle of 15°, the receiver is able to achieve an effective secret key rate (10 −4 bits/pulse) even at 9.71 m depth. Smaller zenith angles and lower wind speeds contribute to an increase in the interface secret key rate.
In the context of secure underwater optical communications, this study examines the performance of the entanglement-based BBM92 protocol when the source generates non-maximally entangled photon pairs. The impact of seawater optical properties, as well as source correlation characteristics, on transmission efficiency is analyzed for three types of nonturbulent channels: clear, coastal, and turbid water. The main performance metrics, including quantum bit error rate (QBER), secret key rate (SKR), and correlation probability, are analytically derived and evaluated as functions of transmission distance between two communicating parties. Monte Carlo simulation results validate our analytical models and quantify performance under different channel conditions.