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arXiv:2507.21546 · Physical Review Letters

Long-Distance Free-Space Quantum Key Distribution with Continuous Variables

Tianxiang Zhan, Huasheng Li, Peng Huang, Haoze Chen, Jiaqi Han, Zijing Wu, Hao Fang, Hanwen Yin, Zehao Zhou, Huiting Fu, Feiyu Ji, Piao Tan, Yingming Zhou, Xueqin Jiang, Tao Wang, Jincai Wu, Cheng Ye, Yajun Miao, Wei Qi, Guihua Zeng

Published Feb 10, 2026• 5 citations
arXivHTMLPDF

Abstract

Continuous-variable quantum key distribution (CVQKD) enables remote users to share high-rate and unconditionally secure secret keys while maintaining compatibility with classical optical communication networks and effective resistance against background noise. However, CVQKD experiments have been demonstrated only indoors or over short outdoor distances. Here, by developing channel-fluctuation-independent high-precision manipulation of continuous-variable quantum states, high-accuracy quantum signal acquisition and processing, and high-efficiency free-space acquisition, tracking, and pointing technology, we overcome the excess noise due to atmospheric effects especially in daylight without extra wavelength conversion and narrow-linewidth spectral filtering and demonstrate for the first time long-distance free-space quantum key distribution under the asymptotic condition over 7-km inland and 9.6-km maritime atmospheric channels with Gaussian-modulated coherent states. Given that the CVQKD system is naturally compatible with existing ground fiber telecommunication networks, it marks an essential step for realizing integrated air-ground quantum access networks with cross-domain applications.

DOI
10.1103/hvhx-pdrn

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Continuous-variable quantum key distribution (CVQKD) enables remote users to share high-rate and unconditionally secure secret keys while maintaining compatibility with classical optical communication networks and effective resistance against background noise. However, CVQKD experiments have been demonstrated only indoors or over short outdoor distances. Here, by developing channel-fluctuation-independent high-precision manipulation of continuous-variable quantum states, high-accuracy quantum signal acquisition and processing, and high-efficiency free-space acquisition, tracking, and pointing technology, we overcome the excess noise due to atmospheric effects especially in daylight without extra wavelength conversion and narrow-linewidth spectral filtering and demonstrate for the first time long-distance free-space quantum key distribution under the asymptotic condition over 7-km inland and 9.6-km maritime atmospheric channels with Gaussian-modulated coherent states. Given that the CVQKD system is naturally compatible with existing ground fiber telecommunication networks, it marks an essential step for realizing integrated air-ground quantum access networks with cross-domain applications.
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Quantum key distribution (QKD) enables two remote parties to share encryption keys with security based on the laws of physics. Continuous-variable (CV) QKD with coherent states and coherent detection integrates well with existing telecommunication networks. Thus far, long-distance CV-QKD has only been demonstrated using a highly complex scheme where the local oscillator is transmitted, opening security loopholes for eavesdroppers and limiting potential applications. Here, we report a long-distance CV-QKD experiment with a locally generated local oscillator over a 100-kilometer fiber channel with a total loss of 15.4 decibels. This record-breaking distance is achieved by controlling the phase noise-induced excess noise through a machine learning framework for carrier recovery and optimizing the modulation variance. We implement the full CV-QKD protocol and demonstrate the generation of keys secure against collective attacks in the finite-size regime. Our results mark a substantial milestone for realizing CV quantum access networks with a high loss budget and pave the way for large-scale deployment of secure QKD.
The advent of quantum computers has significantly challenged the security of traditional cryptographic systems, prompting a surge in research on quantum key distribution (QKD). Among various QKD approaches, continuous-variable QKD (CVQKD) offers superior resilience against background noise. However, the local local oscillator (LLO) CVQKD scheme faces substantial physical limitations in scenarios with high channel attenuation, and the large attenuation CVQKD remains unrealized. Bottleneck challenges include ensuring stable low-noise transmission and accurately estimating parameters under fluctuating channel conditions. We propose a continuous-mode theoretical framework that provides an analytical method for time-varying quantum systems within a free-space channel. This framework can achieve high-fidelity LLO-CVQKD in free space without the need for complex, real-time frequency locking and transmittance calibration equipment. It can also enable free-space QKD under large attenuation and high repetition frequency. Through experimental validation, we first demonstrate high-rate secure quantum key distribution over high-loss free-space channels. Specifically, we achieve asymptotic key rates of 76.366 kbps and 403.896 kbps in 25 dB attenuation free-space channels without turbulence and 21.5 dB average attenuation free-space channels with turbulence, respectively. Additionally, we confirm the feasibility of experiments on mildly turbulent atmospheric channels spanning at least 10.5 km using current equipment. Our scheme provides direct insight into constructing an integrated air-ground quantum communication network.
Continuous variable quantum key distribution (CVQKD) uses the continuous quadratures of light to share a secret key between a transmitter and receiver. The presence of an eavesdropper can be detected by fundamental quantum mechanics. Compared to the more established discrete variable QKD, CVQKD uses more cost-effective homodyne detectors which are more compatible with current telecommunication technologies. In a future global quantum network, CVQKD could be used to ensure the secure exchange of information. In this work, the feasibility of a variety of CVQKD protocols in different channels that could be used to establish a global quantum network are studied. These are the Gaussian modulated and discrete modulated CVQKD protocols for satellite to optical ground station downlinks and uplinks for Earth-space connections, inter-satellite links for space connections, satellite to ship and underwater links for maritime connections, and fibre network links for terrestrial connections. Secret key distribution between continents and various regions is simulated while accounting for the different adverse effects associated with each link. The combination of these connections with routing and scheduling ensures inter-continental high-speed information exchange with unconditional security that is required to achieve the goal of a global quantum network.
Abstract Quantum cryptography communication encompasses both quantum key distribution (QKD) and the encryption and decryption of plaintext. Continuous-variable QKD (CVQKD) leverages the fundamental principles of physics to enable legitimate parties to share secure keys, while the CVQKD-compatible quantum noise stream cipher (QNSC) exploits quantum fluctuations to further obscure the ciphertext encrypted with these keys. Integrating these two functionalities into a unified system represents a promising developmental trend. However, existing integrated architectures typically rely on multiplexing two separate optical paths and have been demonstrated exclusively over optical fibers. Here, a unified local local oscillator (LLO) quantum cryptography architecture operating over a free-space channel is proposed and experimentally demonstrated. Requiring only simple software-defined switching, our payload-efficient architecture executes both CVQKD and QNSC functionalities utilizing a single optical setup. Over an indoor free-space channel with emulated time-varying atmospheric disturbances, an asymptotic secret key rate of 35.4292 kbps is obtained at a maximum channel attenuation of 19.5054 dB for the CVQKD mode. For the QNSC mode, an encrypted image is successfully transmitted, yielding pixel accuracies of 99.58% and 96.39% under channel attenuations of 10.1690 dB and 12.0620 dB, respectively. This work validates the feasibility of integrated quantum cryptography architectures in complex environments, marking a meaningful step toward constructing payload-constrained quantum communication networks.
We propose a novel continuous-variable quantum key distribution (CVQKD) protocol that employs orthogonal frequency-division multiplexing (OFDM) in the terahertz (THz) band to enable high-throughput and secure quantum communication. By encoding quantum information across multiple subcarriers, the protocol enhances spectral efficiency and mitigates channel dispersion and atmospheric attenuation. We present a comprehensive security analysis under collective Gaussian attacks, considering both terrestrial free-space channels, accounting for humidity-induced absorption, and inter-satellite links, incorporating realistic intermodulation noise. Simulations show secret key rates (SKR) reaching ~72 bits per channel use in open-air conditions. While intermodulation noise imposes trade-offs, optimised modulation variance enables resilience and secure communication range. The maximum terrestrial quantum link extends up to 4.5 m due to atmospheric THz absorption, whereas inter-satellite links can support secure communication over distances exceeding 100 km, owing to minimal propagation channel losses in space. We evaluate the practical implementation of our protocol using recently developed on-chip coherent THz sources based on superconducting Josephson junctions. These compact, voltage-tunable emitters produce wideband coherent radiation, making them ideal candidates for integration in scalable quantum networks. By incorporating their characteristics into our simulations, we assess secure key generation under various environmental conditions. Our results show secure communication over distances up to 3 m in open air, and up to 26 km in cryogenic or vacuum environments. This work advances the prospect of compact, high-capacity CVQKD systems for both terrestrial and space-based THz quantum communication.