© 2026 Aqora Quantum S.A.S.

Terms Privacy Legal Notice

Mathematics

Seawater Continuous-Variable Quantum Key Distribution with Orbital Angular Momentum Multiplexing

Lei Mao, Zhangtao Liang, Weihan Zhang, Heng Zhang, Yijun Wang

Published Feb 13, 2026• 0 citations

Abstract

Continuous-Variable Quantum Key Distribution (CVQKD), based on quantum mechanical principles, offers theoretically unconditional security and represents a crucial direction for future secure communications. However, its application in marine environments faces challenges such as high attenuation, scattering, and turbulence in seawater, severely impacting quantum signal transmission and secure key generation efficiency. Orbital angular momentum (OAM) multiplexing technology leverages the orthogonality of photon OAM modes to transmit multiple independent quantum signals in parallel within a single spatial channel. In this scheme, each OAM mode serves as an independent sub-channel, enabling simultaneous key distribution across multiple modes, thereby significantly enhancing the system’s secure key rate and spectral efficiency. This paper proposes an OAM-multiplexed CVQKD scheme tailored for marine channels. Based on Yi’s power spectrum model for marine turbulence refractive index fluctuations, we derive expressions for OAM mode probability density and detection probability. Through system modeling and performance analysis, we investigate the impact of marine turbulence on OAM modes, as well as on the secure key rate and transmission distance of CVQKD systems. Results indicate that higher-order OAM modes exhibit more pronounced turbulence effects, leading to reduced key rates and limited transmission distances. The OAM multiplexing approach significantly enhances system key rates, providing theoretical and technical references for constructing high-rate seawater quantum communication networks.

DOI: 10.3390/math14040660

Related papers

High-Rate Continuous-Variable Quantum Key Distribution with Orbital Angular Momentum Multiplexing

Xinchao Ruan, Wenhao Shi, Guojun Chen +3 more

The secret key rate is one of the main obstacles to the practical application of continuous-variable quantum key distribution (CVQKD). In this paper, we propose a multiplexing scheme to increase the secret key rate of the CVQKD system with orbital angular momentum (OAM). The propagation characteristics of a typical vortex beam, involving the Laguerre-Gaussian (LG) beam, are analyzed in an atmospheric channel for the Kolmogorov turbulence model. Discrete modulation is utilized to extend the maximal transmission distance. We show the effect of the transmittance of the beam over the turbulent channel on the secret key rate and the transmission distance. Numerical simulations indicate that the OAM multiplexing scheme can improve the performance of the CVQKD system and hence has potential use for practical high-rate quantum communications.

Entropy•Sep 9, 2021•5 citations

Passive Continuous Variable Quantum Key Distribution through the Oceanic Turbulence

Yiwu Zhu, Lei Mao, Hui Hu +1 more

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.

Entropy•Feb 7, 2023•4 citations

Parameter estimation of orbital angular momentum based continuous-variable quantum key distribution

Di Jin, Ying Guo, Yijun Wang +1 more

In principle, the number of orbital angular momentum (OAM) eigenstates is unbounded; therefore, OAM multiplexing could greatly increase the transmission rate. Compared with optical fibers, free-space channels fluctuate randomly over time due to the effects of atmospheric turbulence. Free-space channel estimation is necessary. Here, we study the channel parameter estimation of continuous-variable quantum key distribution (CVQKD) based on OAM, especially the influence of atmospheric turbulence on transmittance and excess noise. By comparing the secret key rate in the case of single link and multiplexing, the impact of the estimated parameters on the performance of the CVQKD system is evaluated. Simulation results show that the value of the estimated parameter will affect the secret key rate.

Journal of Applied Physics•Jun 1, 2020•10 citations

Atmospheric continuous-variable quantum secure direct communication with orbital angular momentum multiplexing

Zhengwen Cao, Zhangtao Liang, Yujie Zhang +3 more

Quantum secure direct communication (QSDC) with the feature of allowing secret messages to be communicated directly over quantum channels has two approaches including discrete variable and continuous variable (CV). Among of them, the CVQSDC system indicates the advantages of high secrecy capacity and low experimental cost. As the number of eigenstates is unbounded, the orbital angular momentum (OAM) is an efficient method to increase the secrecy capacity in a CVQSDC system. However, OAM is very vulnerable to atmospheric turbulence, resulting in a phase distortion quantum state. In this work, we propose a CVQSDC protocol with OAM multiplexing, and reveal how the channel parameters, especially transmittance and excess noise, are influenced by atmospheric effects through the simulation experiment. On this basis, the security of the system is further analyzed and the secrecy capacity calculated. The results indicated that the increase in turbulence intensity leads to enhanced crosstalk between the OAM angular modes, which in turn leads to a decrease in the effective transmittance and an increase in the excess noise. Meanwhile, the results also showed that the secrecy capacity decreases with the increase of transmission distance, atmospheric turbulence intensity, and angular mode; in addition, OAM multiplexing can obtain more secrecy capacity compared with a single link.

Journal of the Optical Society of America B•Aug 27, 2024•2 citations

Orbital Angular Momentum Multiplexing for Free-space Quantum Key Distribution Impaired by Turbulence

Yu Chen, Shenjie Huang, Majid Safari

In this paper, a free-space quantum key distribution (QKD) system based on BB84 protocol is studied assuming that the transmitted quantum bits are multiplexed spatially based on orthogonal orbital angular momentum (OAM) carrying beams. The performance of such a system is estimated in terms of quantum bit error rate, outage capacity, and effective data rate taking into account the impact of error correction and privacy amplification. Based on the simulation of OAM-carrying beam propagating through atmospheric channels impaired by turbulence, the crosstalk among the multiplexed channels are investigated and its effect on the performance of the QKD system is evaluated. The presented results provide insight into the efficient design of such multiplexed QKD systems particularly in terms of the choice of the optimal average photon number per pulse and the multiplexing mode set.

International Wireless Communications and Mobile Computing Conference (IWCMC)•Jun 1, 2018•6 citations

Continuous-Variable Quantum Key Distribution Based on N-APSK Modulation over Seawater Channel

Lei Mao, Zhangtao Liang, Zhiyue Zuo +2 more

A continuous-variable quantum key distribution (CVQKD) can be realized over the seawater channel, but the transmission of quantum signals in seawater media exhibits significant attenuation effects. Therefore, we propose an N-symbol amplitude and phase shift keying (N-APSK) modulation scheme to enhance the transmission performance of the CVQKD over the seawater channel. Specifically, an optimal N-APSK modulation scheme is designed based on the principle of maximizing the minimum Euclidean distance (MED). The simulation results show that the CVQKD protocol based on N-APSK modulation achieves a longer transmission distance over the seawater channel compared to the Gaussian modulation protocol. Additionally, increasing the value of N simultaneously expands the number of rings in the constellation diagram, further enhancing the communication distance. This study transfers modulation methods from the field of classical communications to the field of quantum communications, achieving a substantial improvement in communication distance and thereby promoting the integration of quantum communications and classical communications.

Entropy•Sep 22, 2025•0 citations

Continuous-Variable Quantum Key Distribution (CVQKD), based on quantum mechanical principles, offers theoretically unconditional security and represents a crucial direction for future secure communications. However, its application in marine environments faces challenges such as high attenuation, scattering, and turbulence in seawater, severely impacting quantum signal transmission and secure key generation efficiency. Orbital angular momentum (OAM) multiplexing technology leverages the orthogonality of photon OAM modes to transmit multiple independent quantum signals in parallel within a single spatial channel. In this scheme, each OAM mode serves as an independent sub-channel, enabling simultaneous key distribution across multiple modes, thereby significantly enhancing the system’s secure key rate and spectral efficiency. This paper proposes an OAM-multiplexed CVQKD scheme tailored for marine channels. Based on Yi’s power spectrum model for marine turbulence refractive index fluctuations, we derive expressions for OAM mode probability density and detection probability. Through system modeling and performance analysis, we investigate the impact of marine turbulence on OAM modes, as well as on the secure key rate and transmission distance of CVQKD systems. Results indicate that higher-order OAM modes exhibit more pronounced turbulence effects, leading to reduced key rates and limited transmission distances. The OAM multiplexing approach significantly enhances system key rates, providing theoretical and technical references for constructing high-rate seawater quantum communication networks.

The secret key rate is one of the main obstacles to the practical application of continuous-variable quantum key distribution (CVQKD). In this paper, we propose a multiplexing scheme to increase the secret key rate of the CVQKD system with orbital angular momentum (OAM). The propagation characteristics of a typical vortex beam, involving the Laguerre-Gaussian (LG) beam, are analyzed in an atmospheric channel for the Kolmogorov turbulence model. Discrete modulation is utilized to extend the maximal transmission distance. We show the effect of the transmittance of the beam over the turbulent channel on the secret key rate and the transmission distance. Numerical simulations indicate that the OAM multiplexing scheme can improve the performance of the CVQKD system and hence has potential use for practical high-rate quantum communications.

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.

In principle, the number of orbital angular momentum (OAM) eigenstates is unbounded; therefore, OAM multiplexing could greatly increase the transmission rate. Compared with optical fibers, free-space channels fluctuate randomly over time due to the effects of atmospheric turbulence. Free-space channel estimation is necessary. Here, we study the channel parameter estimation of continuous-variable quantum key distribution (CVQKD) based on OAM, especially the influence of atmospheric turbulence on transmittance and excess noise. By comparing the secret key rate in the case of single link and multiplexing, the impact of the estimated parameters on the performance of the CVQKD system is evaluated. Simulation results show that the value of the estimated parameter will affect the secret key rate.

Quantum secure direct communication (QSDC) with the feature of allowing secret messages to be communicated directly over quantum channels has two approaches including discrete variable and continuous variable (CV). Among of them, the CVQSDC system indicates the advantages of high secrecy capacity and low experimental cost. As the number of eigenstates is unbounded, the orbital angular momentum (OAM) is an efficient method to increase the secrecy capacity in a CVQSDC system. However, OAM is very vulnerable to atmospheric turbulence, resulting in a phase distortion quantum state. In this work, we propose a CVQSDC protocol with OAM multiplexing, and reveal how the channel parameters, especially transmittance and excess noise, are influenced by atmospheric effects through the simulation experiment. On this basis, the security of the system is further analyzed and the secrecy capacity calculated. The results indicated that the increase in turbulence intensity leads to enhanced crosstalk between the OAM angular modes, which in turn leads to a decrease in the effective transmittance and an increase in the excess noise. Meanwhile, the results also showed that the secrecy capacity decreases with the increase of transmission distance, atmospheric turbulence intensity, and angular mode; in addition, OAM multiplexing can obtain more secrecy capacity compared with a single link.

In this paper, a free-space quantum key distribution (QKD) system based on BB84 protocol is studied assuming that the transmitted quantum bits are multiplexed spatially based on orthogonal orbital angular momentum (OAM) carrying beams. The performance of such a system is estimated in terms of quantum bit error rate, outage capacity, and effective data rate taking into account the impact of error correction and privacy amplification. Based on the simulation of OAM-carrying beam propagating through atmospheric channels impaired by turbulence, the crosstalk among the multiplexed channels are investigated and its effect on the performance of the QKD system is evaluated. The presented results provide insight into the efficient design of such multiplexed QKD systems particularly in terms of the choice of the optimal average photon number per pulse and the multiplexing mode set.

A continuous-variable quantum key distribution (CVQKD) can be realized over the seawater channel, but the transmission of quantum signals in seawater media exhibits significant attenuation effects. Therefore, we propose an N-symbol amplitude and phase shift keying (N-APSK) modulation scheme to enhance the transmission performance of the CVQKD over the seawater channel. Specifically, an optimal N-APSK modulation scheme is designed based on the principle of maximizing the minimum Euclidean distance (MED). The simulation results show that the CVQKD protocol based on N-APSK modulation achieves a longer transmission distance over the seawater channel compared to the Gaussian modulation protocol. Additionally, increasing the value of N simultaneously expands the number of rings in the constellation diagram, further enhancing the communication distance. This study transfers modulation methods from the field of classical communications to the field of quantum communications, achieving a substantial improvement in communication distance and thereby promoting the integration of quantum communications and classical communications.