Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chinese Physics B

Performance analysis of quantum key distribution using polarized coherent-states in free-space channel

Zengte Zheng, Ziyang Chen, Luyu Huang, Xiangyu Wang, Song Yu

Published May 29, 2022• 6 citations
Publisher

Abstract

In free space channel, continuous-variable quantum key distribution (CV-QKD) using polarized coherent-states can not only make the signal state more stable and less susceptible to interference based on the polarization non-sensitive of the free-space channel, but also reduce the noise introduced by phase interference. However, arbitrary continuous modulation can not be carried out in the past polarization coding, resulting in that the signal state can not obtain arbitrary continuous value in Poincare space, and the security analysis of CV-QKD using polarized coherent-states in free space is not complete. Here we propose a new modulation method to extend the modulation range of signal states with an optical-fiber-based polarization controller. In particular, in terms of the main influence factors in the free-space channel, we utilize the beam extinction and elliptical model when considering the transmittance and adopt the formulation of secret key rate. In addition, the performance of the proposed scheme under foggy weather is also taken into consideration to reveal the influence of severe weather. Numerical simulation shows that the proposed scheme is seriously affected by attenuation under foggy weather. The protocol fails when visibility is less than 1 km. At the same time, the wavelength can affect the performance of the proposed scheme. Specifically, under foggy weather, the longer the wavelength, the smaller the attenuation coefficient, and the better the transmission performance. Our proposed scheme can expand the modulation range of signal state, and supplement the security research of the scheme in the free-space channel, thus can provide theoretical support for subsequent experiments.

DOI
10.1088/1674-1056/ac7450

Related papers

Performance Analysis of Continuous Variable Quantum Key Distribution Over Free Space Optical Channel under Fog Conditions

Ibtihaj Hameed, Shelan Khasro Tawfeeq

Quantum key distribution (QKD) provides secure keys with information-theoretic security ensured by the principles of quantum mechanics. The flexibility and efficient deployment of free-space optical (FSO) quantum key distribution systems can make them highly advantageous. Despite the benefits of free-space transmission, there is still a chance of running into unfavorable weather conditions like fog. According to this study, free-space continuous variable (CV) QKD systems may be applicable when fog is present. Using attenuation based on the Kim and Kruse empirical visibility models, the performance of the models that explain the relationship between fog attenuation and air visibility is examined in order to evaluate its impact on the secure key rate (SKR) at wavelengths of 850 and 1550 nm. A comparative analysis between the two wavelengths is carried out to highlight their suitability under different weather conditions. Based on the results, 1550 nm performs better in foggy situations, reaching an SKR of 1.389379 bits/symbol, because of lower scattering losses, whereas 850 nm achieves a longer range of 12 km in clear air because of smaller diffraction divergence. The results demonstrate that wavelength selection plays a critical role in enhancing the robustness of CV-QKD systems that operate over FSO links. In addition, optimizing reconciliation efficiency (β) under thick-fog conditions greatly improved the SKR, indicating that 1550 nm operation has the ability to achieve reliable and secure quantum communication. Results show that varying β from 0.90 to 1.00 for both 850 nm and 1550 nm produces SKR enhancement of (0.63-0.80 bits/symbol) and (0.97-1.13 bits/symbol), respectively.

Al-Nahrain Journal for Engineering Sciences•Sep 20, 2026•0 citations

Continuous-variable quantum key distribution robust against environmental disturbances

Huanxi Zhao, Tao Wang, Yuehan Xu +5 more

Continuous variable quantum key distribution (CV-QKD) can guarantee that two parties share secure keys even in the presence of an eavesdropper. However, the polarization direction of the coherent state transmitted in CV-QKD is susceptible to environmental disturbances during channel transmission, making it difficult to share keys consistently over long periods of time. Therefore, a CV-QKD system that can resist environmental disturbance is very urgent. In this paper, we propose a new optical architecture for CV-QKD based on the Faraday-Michelson interference (FMI) structure, and finally form an all-single-mode (SM) fiber-based stable CV-QKD system which employs transmitted local oscillator (TLO) scheme and discrete modulation coherent state (DMCS) protocol. Specifically, since the Faraday mirror rotates the polarization direction of light by 90 o , the birefringence effect of light can be effectively dealt with, thus ensuring the same polarization state of light before and after reflection. The final simulation results show that the theoretical secret key rate of this scheme can reach 139 kbps at 70 km, which can further improve the stability and robustness of CV-QKD in the real environment, and provide technical support for the next-generation high-stability QKD system.

Optics Express•Jan 17, 2024•8 citations

Proof-of-principle test of coherent-state continuous variable quantum key distribution through turbulent atmosphere (Conference Presentation)

Ivan D. Derkach, Christian Peuntinger, László Ruppert +7 more

Continuous-variable quantum key distribution is a practical application of quantum information theory that is aimed at generation of secret cryptographic key between two remote trusted parties and that uses multi-photon quantum states as carriers of key bits. Remote parties share the secret key via a quantum channel, that presumably is under control of of an eavesdropper, and which properties must be taken into account in the security analysis. Well-studied fiber-optical quantum channels commonly possess stable transmittance and low noise levels, while free-space channels represent a simpler, less demanding and more flexible alternative, but suffer from atmospheric effects such as turbulence that in particular causes a non-uniform transmittance distribution referred to as fading. Nonetheless free-space channels, providing an unobstructed line-of-sight, are more apt for short, mid-range and potentially long-range (using satellites) communication and will play an important role in the future development and implementation of QKD networks. It was previously theoretically shown that coherent-state CV QKD should be in principle possible to implement over a free-space fading channel, but strong transmittance fluctuations result in the significant modulation-dependent channel excess noise. In this regime the post-selection of highly transmitting sub-channels may be needed, which can even restore the security of the protocol in the strongly turbulent channels. We now report the first proof-of-principle experimental test of coherent state CV QKD protocol using different levels Gaussian modulation over a mid-range (1.6-kilometer long) free-space atmospheric quantum channel. The transmittance of the link was characterized using intensity measurements for the reference but channel estimation using the modulated coherent states was also studied. We consider security against Gaussian collective attacks, that were shown to be optimal against CV QKD protocols . We assumed a general entangling cloner collective attack (modeled using data obtained from the state measurement results on both trusted sides of the protocol), that allows to purify the noise added in the quantum channel . Our security analysis of coherent-state protocol also took into account the effect of imperfect channel estimation, limited post-processing efficiency and finite data ensemble size on the performance of the protocol. In this regime we observe the positive key rate even without the need of applying post-selection. We show the positive improvement of the key rate with increase of the modulation variance, still remaining low enough to tolerate the transmittance fluctuations. The obtained results show that coherent-state CV QKD protocol that uses real free-space atmospheric channel can withstand negative influence of transmittance fluctuations, limited post-processing efficiency, imperfect channel estimation and other finite-size effects, and be successfully implemented. Our result paves the way to the full-scale implementation of the CV QKD in real free-space channels at mid-range distances.

•Dec 7, 2016•2 citations

Free-space continuous-variable quantum key distribution of unidimensional Gaussian modulation using polarized coherent states in an urban environment

Shi-Yang Shen, Mingwei Dai, Xue-Tao Zheng +3 more

An experiment evaluating continuous-variable quantum key distribution (CV-QKD) in an urban environment free-space channel has been accomplished using a single homodyne detector. This is based on Gaussian modulation with coherent states in the polarization degree of freedom. We achieved a QKD distance at 460 m at a repetition rate of 10 kHz. The secure key rate is 0.152 kbps at the typical reconciliation efficiency of 0.95. The experimental setup of this scheme is simplified, and the barrier for implementation has been remarkably reduced compared to that for traditional symmetric modulation protocols, for example, the GG02 protocol proposed in F. Grosshans and P. Grangier [Phys. Rev. Lett. 88, 057902 (2002)]. The influence of the security key rate by asymmetric modulation is small for a relatively low channel loss condition in a free-space environment. This scheme is expected to have significance for future practical applications.

arXiv:1810.00408•Physical Review A•Jul 16, 2019•52 citations

Microwave continuous-variable quantum key distribution in the open air

Y. Feng, Gang Xu, Xiu‐Bo Chen +1 more

Continuous-variable quantum key distribution (CV-QKD) enables the efficient distribution of unconditionally secure keys for both communicating parties. Despite significant advancements in optical-based CV-QKD, a persistent challenge is the limited resilience of optical quantum signals to atmospheric noise in free-space channels. This susceptibility leads to considerable degradation in the performance of optical CV-QKD systems, particularly under adverse climatic conditions. Meanwhile, recent advancements in superconducting quantum computing have driven the demand for quantum communication between spatially separated superconducting processors operating at microwave frequencies. To solve the problems, we propose a Gaussian-modulated coherent-state protocol operating at microwave frequencies, utilizing traveling-wave parametric amplifiers to generate entangled states. Our numerical analysis demonstrates that CV-QKD at microwave frequencies enables secure communication in a free-space channel at room temperature. Furthermore, we show that this protocol outperforms the THz frequency protocol over a distance of 20 m and exhibits stronger immunity to interference. Finally, we consider the impact of microwave antenna gain on the protocol's performance, highlighting the decisive role of antenna gain in determining the maximum transmission distance in practical application scenarios.

Physical Review A•Apr 30, 2025•0 citations

Free-space Continuous-Variable Quantum Key Distribution in moderate and strong atmospheric turbulence

Hailong Zhang, Xingran Chen, Jianhong Shi

Abstract Quantum Key Distribution (QKD) has been widely applied due to its theoretical one-time pad encryption. Typically employing laser beam as carrier, quantum states are transmitted through optical fibers or free-space channels, with the latter being more commonly adopted. However, compared to optical fibers, free-space links are more susceptible to external environmental factors, particularly atmospheric conditions. Beam propagation through the atmosphere experiences diffraction, refraction, and intensity attenuation, which can degrade key distribution efficiency and even prevent key generation at the receiver. The atmospheric turbulence poses the most significant challenge in all influencing factors, especially for the commonly encountered moderate-to-strong turbulence regimes. Therefore, in this work, we develop a phase screen model and turbulence-dominated transmittance model to comprehensively investigate the impact of various key parameters on optical beam propagation through turbulent atmospheres. Furthermore, we derive the key rate for the CV-QKD protocol using a TMSV (two-mode squeezed vacuum) state and perform numerical simulations.

Chinese Physics B•May 11, 2026•0 citations
In free space channel, continuous-variable quantum key distribution (CV-QKD) using polarized coherent-states can not only make the signal state more stable and less susceptible to interference based on the polarization non-sensitive of the free-space channel, but also reduce the noise introduced by phase interference. However, arbitrary continuous modulation can not be carried out in the past polarization coding, resulting in that the signal state can not obtain arbitrary continuous value in Poincare space, and the security analysis of CV-QKD using polarized coherent-states in free space is not complete. Here we propose a new modulation method to extend the modulation range of signal states with an optical-fiber-based polarization controller. In particular, in terms of the main influence factors in the free-space channel, we utilize the beam extinction and elliptical model when considering the transmittance and adopt the formulation of secret key rate. In addition, the performance of the proposed scheme under foggy weather is also taken into consideration to reveal the influence of severe weather. Numerical simulation shows that the proposed scheme is seriously affected by attenuation under foggy weather. The protocol fails when visibility is less than 1 km. At the same time, the wavelength can affect the performance of the proposed scheme. Specifically, under foggy weather, the longer the wavelength, the smaller the attenuation coefficient, and the better the transmission performance. Our proposed scheme can expand the modulation range of signal state, and supplement the security research of the scheme in the free-space channel, thus can provide theoretical support for subsequent experiments.
Quantum key distribution (QKD) provides secure keys with information-theoretic security ensured by the principles of quantum mechanics. The flexibility and efficient deployment of free-space optical (FSO) quantum key distribution systems can make them highly advantageous. Despite the benefits of free-space transmission, there is still a chance of running into unfavorable weather conditions like fog. According to this study, free-space continuous variable (CV) QKD systems may be applicable when fog is present. Using attenuation based on the Kim and Kruse empirical visibility models, the performance of the models that explain the relationship between fog attenuation and air visibility is examined in order to evaluate its impact on the secure key rate (SKR) at wavelengths of 850 and 1550 nm. A comparative analysis between the two wavelengths is carried out to highlight their suitability under different weather conditions. Based on the results, 1550 nm performs better in foggy situations, reaching an SKR of 1.389379 bits/symbol, because of lower scattering losses, whereas 850 nm achieves a longer range of 12 km in clear air because of smaller diffraction divergence. The results demonstrate that wavelength selection plays a critical role in enhancing the robustness of CV-QKD systems that operate over FSO links. In addition, optimizing reconciliation efficiency (β) under thick-fog conditions greatly improved the SKR, indicating that 1550 nm operation has the ability to achieve reliable and secure quantum communication. Results show that varying β from 0.90 to 1.00 for both 850 nm and 1550 nm produces SKR enhancement of (0.63-0.80 bits/symbol) and (0.97-1.13 bits/symbol), respectively.
Continuous variable quantum key distribution (CV-QKD) can guarantee that two parties share secure keys even in the presence of an eavesdropper. However, the polarization direction of the coherent state transmitted in CV-QKD is susceptible to environmental disturbances during channel transmission, making it difficult to share keys consistently over long periods of time. Therefore, a CV-QKD system that can resist environmental disturbance is very urgent. In this paper, we propose a new optical architecture for CV-QKD based on the Faraday-Michelson interference (FMI) structure, and finally form an all-single-mode (SM) fiber-based stable CV-QKD system which employs transmitted local oscillator (TLO) scheme and discrete modulation coherent state (DMCS) protocol. Specifically, since the Faraday mirror rotates the polarization direction of light by 90 o , the birefringence effect of light can be effectively dealt with, thus ensuring the same polarization state of light before and after reflection. The final simulation results show that the theoretical secret key rate of this scheme can reach 139 kbps at 70 km, which can further improve the stability and robustness of CV-QKD in the real environment, and provide technical support for the next-generation high-stability QKD system.
Continuous-variable quantum key distribution is a practical application of quantum information theory that is aimed at generation of secret cryptographic key between two remote trusted parties and that uses multi-photon quantum states as carriers of key bits. Remote parties share the secret key via a quantum channel, that presumably is under control of of an eavesdropper, and which properties must be taken into account in the security analysis. Well-studied fiber-optical quantum channels commonly possess stable transmittance and low noise levels, while free-space channels represent a simpler, less demanding and more flexible alternative, but suffer from atmospheric effects such as turbulence that in particular causes a non-uniform transmittance distribution referred to as fading. Nonetheless free-space channels, providing an unobstructed line-of-sight, are more apt for short, mid-range and potentially long-range (using satellites) communication and will play an important role in the future development and implementation of QKD networks. It was previously theoretically shown that coherent-state CV QKD should be in principle possible to implement over a free-space fading channel, but strong transmittance fluctuations result in the significant modulation-dependent channel excess noise. In this regime the post-selection of highly transmitting sub-channels may be needed, which can even restore the security of the protocol in the strongly turbulent channels. We now report the first proof-of-principle experimental test of coherent state CV QKD protocol using different levels Gaussian modulation over a mid-range (1.6-kilometer long) free-space atmospheric quantum channel. The transmittance of the link was characterized using intensity measurements for the reference but channel estimation using the modulated coherent states was also studied. We consider security against Gaussian collective attacks, that were shown to be optimal against CV QKD protocols . We assumed a general entangling cloner collective attack (modeled using data obtained from the state measurement results on both trusted sides of the protocol), that allows to purify the noise added in the quantum channel . Our security analysis of coherent-state protocol also took into account the effect of imperfect channel estimation, limited post-processing efficiency and finite data ensemble size on the performance of the protocol. In this regime we observe the positive key rate even without the need of applying post-selection. We show the positive improvement of the key rate with increase of the modulation variance, still remaining low enough to tolerate the transmittance fluctuations. The obtained results show that coherent-state CV QKD protocol that uses real free-space atmospheric channel can withstand negative influence of transmittance fluctuations, limited post-processing efficiency, imperfect channel estimation and other finite-size effects, and be successfully implemented. Our result paves the way to the full-scale implementation of the CV QKD in real free-space channels at mid-range distances.
An experiment evaluating continuous-variable quantum key distribution (CV-QKD) in an urban environment free-space channel has been accomplished using a single homodyne detector. This is based on Gaussian modulation with coherent states in the polarization degree of freedom. We achieved a QKD distance at 460 m at a repetition rate of 10 kHz. The secure key rate is 0.152 kbps at the typical reconciliation efficiency of 0.95. The experimental setup of this scheme is simplified, and the barrier for implementation has been remarkably reduced compared to that for traditional symmetric modulation protocols, for example, the GG02 protocol proposed in F. Grosshans and P. Grangier [Phys. Rev. Lett. 88, 057902 (2002)]. The influence of the security key rate by asymmetric modulation is small for a relatively low channel loss condition in a free-space environment. This scheme is expected to have significance for future practical applications.
Continuous-variable quantum key distribution (CV-QKD) enables the efficient distribution of unconditionally secure keys for both communicating parties. Despite significant advancements in optical-based CV-QKD, a persistent challenge is the limited resilience of optical quantum signals to atmospheric noise in free-space channels. This susceptibility leads to considerable degradation in the performance of optical CV-QKD systems, particularly under adverse climatic conditions. Meanwhile, recent advancements in superconducting quantum computing have driven the demand for quantum communication between spatially separated superconducting processors operating at microwave frequencies. To solve the problems, we propose a Gaussian-modulated coherent-state protocol operating at microwave frequencies, utilizing traveling-wave parametric amplifiers to generate entangled states. Our numerical analysis demonstrates that CV-QKD at microwave frequencies enables secure communication in a free-space channel at room temperature. Furthermore, we show that this protocol outperforms the THz frequency protocol over a distance of 20 m and exhibits stronger immunity to interference. Finally, we consider the impact of microwave antenna gain on the protocol's performance, highlighting the decisive role of antenna gain in determining the maximum transmission distance in practical application scenarios.
Abstract Quantum Key Distribution (QKD) has been widely applied due to its theoretical one-time pad encryption. Typically employing laser beam as carrier, quantum states are transmitted through optical fibers or free-space channels, with the latter being more commonly adopted. However, compared to optical fibers, free-space links are more susceptible to external environmental factors, particularly atmospheric conditions. Beam propagation through the atmosphere experiences diffraction, refraction, and intensity attenuation, which can degrade key distribution efficiency and even prevent key generation at the receiver. The atmospheric turbulence poses the most significant challenge in all influencing factors, especially for the commonly encountered moderate-to-strong turbulence regimes. Therefore, in this work, we develop a phase screen model and turbulence-dominated transmittance model to comprehensively investigate the impact of various key parameters on optical beam propagation through turbulent atmospheres. Furthermore, we derive the key rate for the CV-QKD protocol using a TMSV (two-mode squeezed vacuum) state and perform numerical simulations.