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Advanced Quantum Technologies

Coordinated Suppression of Excess Noise for Continuous‐Variable Quantum Key Distribution in Unstable Channels Via Ensemble Learning

Kexin Liang, Zhengwen Cao, Geng Chai

Published Sep 1, 2026• 0 citations
Publisher

Abstract

ABSTRACT Excess noise is a critical factor limiting the system performance of Continuous‐Variable Quantum Key Distribution (CVQKD). However, conventional suppression methods are optimized for a single type of excess noise and exhibit insufficient robustness in unstable channels, reducing the improvement of the secret key rate (SKR). Thus, this work proposes an ensemble learning‐based excess noise suppression framework. By fusing decision information from multiple submodels, ensemble learning frees the framework from the limitation of relying on a single excess noise distribution, enabling it to adapt to the characteristic differences of excess noise from diverse sources and ultimately achieve coordinated suppression of multi‐source excess noise. To further enhance the real‐time adaptability of the framework to unstable channels, the Grey Wolf Optimizer (GWO) is introduced to optimize the hyperparameters of the ensemble learning model globally, ensuring the model can maintain stable suppression performance under changing channel environments. Experiments demonstrate that this scheme enables the centralized suppression of excess noise within the system, with a maximum suppression rate of 75%. The SKR is significantly improved by approximately 2.43 times, which verifies the effectiveness of the scheme in enhancing the system's performance.

DOI
10.1002/qute.70448

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ABSTRACT Excess noise is a critical factor limiting the system performance of Continuous‐Variable Quantum Key Distribution (CVQKD). However, conventional suppression methods are optimized for a single type of excess noise and exhibit insufficient robustness in unstable channels, reducing the improvement of the secret key rate (SKR). Thus, this work proposes an ensemble learning‐based excess noise suppression framework. By fusing decision information from multiple submodels, ensemble learning frees the framework from the limitation of relying on a single excess noise distribution, enabling it to adapt to the characteristic differences of excess noise from diverse sources and ultimately achieve coordinated suppression of multi‐source excess noise. To further enhance the real‐time adaptability of the framework to unstable channels, the Grey Wolf Optimizer (GWO) is introduced to optimize the hyperparameters of the ensemble learning model globally, ensuring the model can maintain stable suppression performance under changing channel environments. Experiments demonstrate that this scheme enables the centralized suppression of excess noise within the system, with a maximum suppression rate of 75%. The SKR is significantly improved by approximately 2.43 times, which verifies the effectiveness of the scheme in enhancing the system's performance.
Abstract The excess noise inducing in the process of the quantum communication procedure is the major obstacle restricting the performance of continuous-variable quantum key distribution (CVQKD). In order to effectively suppress the excess noise through correcting the propagation-induced distortions on the quality of the propagated quantum signal, we propose a general scheme of suppressing excess noise for CVQKD via adaptive optics (AO) approach. The analysis shows that phase-only AO compensation exhibits excellent performance in controlling the excess noise, which is embodied in substantially extending the secure propagation distance and improving the secret key rate of the system. And thereby the development and improvement of AO has the potential advantage to break the distance constraints due to the excess noise results from propagation-dominated factors. Our scheme provides a feasible method for further implementation of practical large-scale CVQKD.
Excess noise is a major obstacle to high-performance continuous-variable quantum key distribution (CVQKD), which is mainly derived from the amplitude attenuation and phase fluctuation of quantum signals caused by channel instability. Here, an excess noise suppression scheme based on equalization is proposed. In this scheme, the distorted signals can be corrected through equalization assisted by a neural network and pilot tone, relieving the pressure on the post-processing and eliminating the hardware cost. For a free-space channel with more intense fluctuation, a classification algorithm is added to classify the received variables, and then the distinctive equalization correction for different classes is carried out. The experimental results show that the scheme can suppress the excess noise to a lower level, and has a significant performance improvement. Moreover, the scheme also enables the system to cope with strong turbulence. It breaks the bottleneck of long-distance quantum communication and lays a foundation for the large-scale application of CVQKD.
Abstract Parameter estimation is a critical step in continuous-variable quantum key distribution (CV-QKD), as the statistical uncertainty from a finite data size leads to pessimistic worst-case bounds that drastically reduce the secret key rate and range. While machine learning techniques have been proposed for this task, they have lacked the rigorous statistical framework necessary for integration into a composable security proof. In this work, we bridge this gap by introducing a statistically rigorous framework for using neural networks for parameter estimation in CV-QKD with quantifiable composable security. We develop a neural network estimator for the excess noise and, crucially, derive its worst-case confidence interval using a delta method approach, ensuring the estimation fails with a probability not exceeding ε PE . This allows the network to be integrated into a parameter estimation protocol that is operationally equivalent to the standard maximum likelihood method but yields significantly tighter parameter bounds. Our numerical results demonstrate that this method provides substantially more precise estimates, which directly translates into a higher secret key rate and extended transmission distance over a fiber channel under a collective Gaussian attack. This work establishes that machine learning can be securely and effectively harnessed to overcome a key performance limitation in practical CV-QKD systems.
Continuous-variable quantum key distribution (CV-QKD) is a promising protocol that can be easily integrated with classical optical communication systems. However, in the case of quantum-classical co-transmissions, such as dense wavelength division multiplexing with classical channels and time division multiplexing with large-power classical signal, a quantum signal is more susceptible to crosstalk caused by a classical signal, leading to signal distortion and key distribution performance reduction. To address this issue, we propose a noise-suppression scheme based on carrier frequency switching (CFS) that can effectively mitigate the influence of large-power random noise on the weak coherent state. In this noise-suppression scheme, a minimum-value window of the channel's noise power spectrum is searched for and the transmission signal frequency spectrum shifts to the corresponding frequency to avoid large-power channel noise. A digital filter is also utilized to filter out most of the channel noise. Simulation results show that compared to the traditional fixed carrier frequency scheme, the proposed noise-suppression scheme can reduce the excess noise to 1.8%, and the secret key rate can be increased by 1.43 to 2.86 times at different distances. This noise-suppression scheme is expected to be applied in scenarios like quantum-classical co-transmission and multi-QKD co-transmission to provide noise-suppression solutions.
Abstract We address the crucial role of noisy squeezing in security and performance of continuous-variable (CV) quantum key distribution (QKD) protocols. Squeezing has long been recognized for its numerous advantages in CV QKD, such as enhanced robustness against channel noise and loss, and improved secret key rates. However, the excess noise of the squeezed states, that unavoidably originates already from optical loss as well as other imperfections in the source, raises concerns about its potential exploitation by an eavesdropper. For the widely adopted trust assumption on the excess noise in the signal states, we confirm the stability of the protocol against the noisy squeezing in both purely attenuating as well as noisy channels in the asymptotic limit, which implies perfect parameter estimation. In the finite-size regime we show that this stability largely holds at up to 107 data points using optimal biased homodyne detection for key distribution and parameter estimation. Untrusted assumption on the noisy squeezing, on the other hand, introduces additional security bounds on the squeezing excess noise already in the asymptotic regime, which is further enforced by the finite-size effects. Additionally, we show the critical negative role of noisy squeezing in the case of atmospheric free-space channels, already in the trusted-noise and asymptotic assumptions, which emphasizes the importance of squeezing purity in the free-space quantum channels. Our results pave the way towards practical realization of squeezed-state CV QKD protocols in both fibre and free-space channels.
Abstract We address the crucial role of noisy squeezing in security and performance of continuous-variable (CV) quantum key distribution (QKD) protocols. Squeezing has long been recognized for its numerous advantages in CV QKD, such as enhanced robustness against channel noise and loss, and improved secret key rates. However, the excess noise of the squeezed states, that unavoidably originates already from optical loss as well as other imperfections in the source, raises concerns about its potential exploitation by an eavesdropper. For the widely adopted trust assumption on the excess noise in the signal states, we confirm the stability of the protocol against the noisy squeezing in both purely attenuating as well as noisy channels in the asymptotic limit, which implies perfect parameter estimation. In the finite-size regime we show that this stability largely holds at up to 107 data points using optimal biased homodyne detection for key distribution and parameter estimation. Untrusted assumption on the noisy squeezing, on the other hand, introduces additional security bounds on the squeezing excess noise already in the asymptotic regime, which is further enforced by the finite-size effects. Additionally, we show the critical negative role of noisy squeezing in the case of atmospheric free-space channels, already in the trusted-noise and asymptotic assumptions, which emphasizes the importance of squeezing purity in the free-space quantum channels. Our results pave the way towards practical realization of squeezed-state CV QKD protocols in both fibre and free-space channels.