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Free-space continuous-variable quantum key distribution under high background noise

Xue-Tao Zheng, Qi-Fa Zhang, Jie Ling, Guang‐Can Guo, Zheng‐Fu Han

Published Mar 27, 2025• 26 citations
Publisher

Abstract

Abstract One of the difficulties in the application of quantum communication is the fragility of its encoded quantum states. Conventional quantum key distribution (QKD) requires strict filtering operations at the receiver. Any ambient light entering the system can significantly increase the bit error rate and even render the system inoperable. We present a continuous-variable quantum key distribution (CV-QKD) system that can function effectively during the day or even on rainy days without complex filtering operations. The Gaussian modulated coherent state continuous-variable quantum key distribution (GMCS CV-QKD) system demonstrates robustness, maintaining a secure key rate (SKR) of more than 100 kbps when operating at a frequency of 10 MHz, which lays the foundation for low-cost, highly robust free-space quantum communication.

DOI
10.1038/s41534-025-01009-w

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Abstract One of the difficulties in the application of quantum communication is the fragility of its encoded quantum states. Conventional quantum key distribution (QKD) requires strict filtering operations at the receiver. Any ambient light entering the system can significantly increase the bit error rate and even render the system inoperable. We present a continuous-variable quantum key distribution (CV-QKD) system that can function effectively during the day or even on rainy days without complex filtering operations. The Gaussian modulated coherent state continuous-variable quantum key distribution (GMCS CV-QKD) system demonstrates robustness, maintaining a secure key rate (SKR) of more than 100 kbps when operating at a frequency of 10 MHz, which lays the foundation for low-cost, highly robust free-space quantum communication.
Future global quantum communication networks, or quantum internet, will realize high-rate secure communication and entanglement distribution for large-scale users over long distances. Continuous variable (CV) quantum key distribution (QKD) provides a powerful setting for secure quantum communications, thanks to the use of room-temperature off-the-shelf optical devices and the potential to reach high rates. However, the achievable performance of CV-QKD protocols is fundamentally limited by the fact that they appear to be fragile to both loss and noise. In this study, we provide a general framework for analyzing the composable finite-size security of CV-QKD with Gaussian-modulated coherent-state (GMCS) protocol under various levels of trust for the loss and noise experienced by the users of the protocol. Our work is comprehensive of several practical scenarios, encompassing both active and passive eavesdropping configurations, with both wired (i.e., fiber-based) and wireless (i.e., free-space and satellite-based) quantum communication channels. Our numerical results evaluate the robustness of the GMCS protocol under varying levels of trust and demonstrate that it is difficult for a practical protocol to remain robust against untrusted loss at the transmitter. In the wireless case, we analyze a scenario with a sun-synchronous satellite, showing that its key distribution rate, even with the worst level of trust, can outperform a ground chain of ideal quantum repeaters. Our results indicate that—when it comes to engineering and optimizing quantum-safe networks—it is essential to mitigate the shortcomings caused by critical trade-offs between rate performance, trust level, system noise, and communication distance.
We experimentally demonstrated a sub-Mbps key rate Gaussian-modulated coherent-state (GMCS) continuous-variable quantum key distribution (CV-QKD) over a 100-km transmission distance. To efficiently control the excess noise, the quantum signal and the pilot tone are co-transmitted in the fiber channel based on wideband frequency and polarization multiplexing methods. Furthermore, a high-accuracy data-assisted time domain equalization algorithm is carefully designed to compensate the phase noise and polarization variation in low signal-to-noise ratio. The asymptotic secure key rate (SKR) of the demonstrated CV-QKD is experimentally calculated to be 7.55 Mbps, 1.87 Mbps, and 0.51 Mbps over a transmission distance of 50 km, 75 km, and 100 km, respectively. The experimentally demonstrated that the CV-QKD system significantly improves the transmission distance and SKR compared to the state-of-art GMCS CV-QKD experimental results, and shows the potential for long-distance and high-speed secure quantum key distribution.
Continuous-variable quantum key distribution (CV-QKD), which uses quadratures of the electromagnetic field, enables practical quantum communication using standard telecommunication technologies. Unidimensional CV-QKD (UD-CVQKD) simplifies the implementation by restricting modulation to a single quadrature. In this work, we experimentally demonstrate a free-space Gaussian-modulated UD-CVQKD system operating under a high detector electronic-noise regime (1.4 shot-noise units). The system employs polarized coherent states with signal and local oscillator co-propagating in the same spatial mode in orthogonal polarizations, ensuring stable interference. System security is analyzed under both untrusted (UTD) and trusted (TD) detector noise models. While no positive secret key rate is obtained under the UTD model, the TD model enables secure key generation over a finite range of modulation variances, highlighting the critical role of detector trust in high-noise conditions. A maximum secret key rate of 270 kbps is achieved at an optimal modulation variance of 11.57. Furthermore, secure operation requires high-transmittance (low-loss) channels under such noise conditions. This study demonstrates the practical feasibility of free-space UD-CVQKD in realistic high electronic-noise detection constraints and highlights detector electronic noise as a key limiting factor in practical systems.
We evaluate the performance of Gaussian Modulated Coherent State (GMCS) Continuous-Variable Quantum Key Distribution (CV-QKD), in terms of secure key rate, at different detector bandwidths. We illustrate the advantages and limitations of high-speed CV-QKD systems using a general noise model in which we consider various noise sources and their dependence upon detection bandwidth. Experimentally, the feasibility of high speed CV-QKD is demonstrated by using a GHz bandwidth balanced homodyne detector (BHD) established with commercially available components. We provide secure key rates of transmitted and local local oscillator schemes under various clock rates.
Abstract Quantum key distribution (QKD) is one quantum technology that can provide secure encryption keys for data transmission. The secret key rate (SKR) is a core performance indicator in QKD, which directly determines the transmission rate of enciphered data. Here, for the first time, we demonstrate a high-key-rate Gaussian-modulated continuous-variable QKD (CV-QKD) using telecom optical components. The framework of CV-QKD over these components is constructed. Specifically, the high-rate low-noise Gaussian modulation of coherent states is realized by a classical optical IQ modulator. High-baud low-intensity quantum signals are received by an integrated coherent receiver under the shot-noise limit. A series of digital signal processing algorithms are proposed to achieve accurate signal recovery and key distillation. The system can yield a high asymptotic SKR of 10.37 Mbps within 20 km standard telecom fiber, and the secure distance can exceed 100 km. This result confirms the feasibility of CV-QKD with state-of-the-art performance using telecom optical components. Besides, due to the ease of integrating these discrete components, it provides a high-performance and miniaturized QKD solution for the metropolitan quantum network.
Continuous-variable quantum key distribution (CV-QKD) is a protocol that uses quantum mechanics to ensure that the distribution of an encryption key is secure even in the presence of eavesdroppers. The wide application of CV-QKD requires low cost, system simplicity, and system stability. However, owing to the particularity of Gaussian modulation in CV-QKD, an amplitude modulator (AM) and a bias controller are required, making the system structure complex and unstable. In this Letter, we achieve two-dimensional Gaussian modulation with only one phase modulator (PM) and a Sagnac ring structure, which significantly reduces the complexity of the system. We test the Gaussian modulation stability for 10 h, and the result shows that the expected secure key rate can be maintained at 80 kbit/s under a transmission distance of 50 km. This scheme opens up new, to the best of our knowledge, possibilities for a new generation of highly stable and simple CV-QKD systems.