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Symmetry

High-Performance Carrier Phase Recovery for Local Local Oscillator Continuous-Variable Quantum Key Distribution

Jiayu Ma, Chao Zhou, Dengke Qi, Ziyang Chen, Yongmei Sun, Song Yu, Xiangyu Wang

Published Jan 18, 2025• 3 citations
Publisher

Abstract

Continuous-variable quantum key distribution (CV-QKD) has been increasingly studied, which offers the advantage of compatibility with modern coherent optical communication systems. In contrast to CV-QKD with a transmitting local oscillator, the local local oscillator CV-QKD avoids the security vulnerabilities of a local oscillator by generating a local oscillator at the receiver. In practice, the frequency offset of the two lasers introduces extra phase noise, which is generally suppressed by various carrier phase recovery algorithms. However, the accuracy of carrier phase recovery can be influenced by the power of the pilot tone, particularly as the transmission distance increases. To further improve accuracy, we propose a method based on the unscented particle filter algorithm, to increase the accuracy of phase estimation, effectively restore the quantum signal and reduce excess noise. In our work, we demonstrated a local local oscillator CV-QKD experiment with a finite-size block of 1×108 under a transmission distance of 50 km. Through our method, we achieved a secret key rate of 525 kbps, which represents a 28% improvement. These results confirm that our proposed method not only improves the accuracy of carrier phase recovery, but also provides a new approach for future research on algorithms for long-distance CV-QKD. Furthermore, our study improves the phase compensation performance, enabling the orthogonal components of the quantum signal to exhibit enhanced symmetry in phase space.

DOI
10.3390/sym17010139

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Continuous-variable quantum key distribution (CV-QKD) has been increasingly studied, which offers the advantage of compatibility with modern coherent optical communication systems. In contrast to CV-QKD with a transmitting local oscillator, the local local oscillator CV-QKD avoids the security vulnerabilities of a local oscillator by generating a local oscillator at the receiver. In practice, the frequency offset of the two lasers introduces extra phase noise, which is generally suppressed by various carrier phase recovery algorithms. However, the accuracy of carrier phase recovery can be influenced by the power of the pilot tone, particularly as the transmission distance increases. To further improve accuracy, we propose a method based on the unscented particle filter algorithm, to increase the accuracy of phase estimation, effectively restore the quantum signal and reduce excess noise. In our work, we demonstrated a local local oscillator CV-QKD experiment with a finite-size block of 1×108 under a transmission distance of 50 km. Through our method, we achieved a secret key rate of 525 kbps, which represents a 28% improvement. These results confirm that our proposed method not only improves the accuracy of carrier phase recovery, but also provides a new approach for future research on algorithms for long-distance CV-QKD. Furthermore, our study improves the phase compensation performance, enabling the orthogonal components of the quantum signal to exhibit enhanced symmetry in phase space.
Quantum key distribution depending on the principles of quantum mechanics, enables secure data exchange by allowing two users to generate a shared random secret key. As a subtype of quantum key distribution, continuous variable quantum key distribution (CV-QKD) has gained prominence due to its easy integration with traditional coherent optical communication. In practice, the effectiveness of phase compensation significantly impacts both excess noise levels and the generation of secret key rates. Therefore, precise phase compensation, also known as carrier recovery, is important to the overall CV-QKD. Hence, accurate carrier recovery is critical for optimal CV-QKD performance. This work simulates a local local oscillator CV-QKD system and introduces an Unscented Kalman Filter algorithm to enhance phase estimation. The results shows that a secret key rate of 229.5 kbps is achievable over a 300m transmission distance with direct reconciliation.
Local local oscillator (LLO) continuous-variable quantum key distribution (CVQKD) schemes have been extensively studied for their enhanced security and simplified system implementation. However, such schemes typically require numerous pilot signals to compensate for phase drift caused by two independent lasers, which significantly increases system overhead and limits the achievable secret key rate. In this work, we propose an enhanced-rate CVQKD scheme, which aims to enhance the secret key rate by achieving high-accuracy phase compensation based on a particle filter (PF) algorithm under low system overhead. Specifically, to counter the loss in phase estimation accuracy due to the reduced number of pilot signals, we introduce a PF-based carrier phase recovery algorithm, complemented by an exponentially weighted phase prediction method to improve phase estimation accuracy. This approach effectively suppresses excess noise under limited pilot information and improves phase compensation precision. Experimental results demonstrate that, compared to the traditional scheme with a 1:1 signal-to-pilot number ratio, our method achieves its maximum performance with a signal-to-pilot number ratio of 3:1, while maintaining phase compensation accuracy virtually unchanged, reducing system overhead by 50% and achieving a 147% improvement in the secret key rate, reaching 235 kbps in a 30 km standard fiber link.
Abstract The secret key rate of a continuous-variable quantum key distribution (CV-QKD) system is limited by excess noise. A key issue typical to all modern CV-QKD systems implemented with a reference or pilot signal and an independent local oscillator is controlling the excess noise generated from the frequency and phase noise accrued by the transmitter and receiver. Therefore accurate phase estimation and compensation, so-called carrier recovery, is a critical subsystem of CV-QKD. Here, we explore the implementation of a machine learning framework based on Bayesian inference, namely an unscented Kalman filter (UKF), for estimation of phase noise and compare it to a standard reference method and a previously demonstrated machine learning method. Experimental results obtained over a 20-km fibre-optic link indicate that the UKF can ensure very low excess noise even at low pilot powers. The measurements exhibited low variance and high stability in excess noise over a wide range of pilot signal to noise ratios. This may enable CV-QKD systems with low hardware implementation complexity which can seamlessly work on diverse transmission lines.
Quantum key distribution relying on the principles of quantum mechanics enables two parties to produce a shared random secret key, thereby ensuring the security of data transmission. Continuous variable quantum key distribution (CV-QKD) is widely applied because it can be well combined with standard telecommunication technology. Compared to CV-QKD with a transmitting local oscillator, the proposal of CV-QKD with a local local oscillator overcomes the limitation that local oscillator will attenuate as transmission distance increases, providing new possibilities in long-distance transmission. However, challenges still persist in practical long-distance transmission, including data sampling and recovery under low signal-to-noise ratio conditions. In order to better recover data and reduce the additional excess noise, we propose the least squares fitting algorithm to get more accurate sampling data and complete more accurate phase compensation.Herein, we demonstrate the long-distance local local oscillator CV-QKD experiment which have considered the effect of finite-size block over 120 km of standard optical fiber with high efficient real-time post-processing. The results not only verify the good performance of the system over long distance, but also paves the way for large-scale quantum secure communications in the future.
Continuous-variable quantum key distribution (CV-QKD) holds promise for enhancing security in communication networks. However, obtaining a higher secure key rate poses challenges, particularly in reliable phase estimation. So, it is very necessary for CV-QKD implementations with independent local oscillator (LO) to employ carrier recovery along with precise phase estimation. Our methodology combines extended Kalman filters (EKF) with recurrent neural networks (RNNs) to enhance the accuracy of phase recovery for locally generated LO signals. Using numerical simulations, we evaluate the achievable secret key rates for different transmission distances and line widths. The proposed method achieves a phase error of approximately 1 × 10–4, leading to positive secure key rates for distances up to 40 km. This method of phase tracking solves the problem and is effective in real-time deployment of CV-QKD in communication networks.
Phase recovery is a key enabling process in continuous-variable quantum key distribution (CV-QKD) systems operating at ultra-low optical power, where phase noise from the finite linewidths of the transmitter and local oscillator lasers critically impacts system performance. Here, we investigate the performance of a phase recovery scheme for a prepare-and-measure CV-QKD setup using the Viterbi–Viterbi carrier phase estimation algorithm. We experimentally evaluate the scheme by varying the power of a binary phase shift keying (BPSK)-modulated pilot tone, using laser sources with nominal linewidths of 1 kHz and 25 kHz. Our results reveal a well-defined operational regime in which stable phase recovery is achieved, as well as a critical threshold below which pilot tone power becomes insufficient, leading to signal distortion and phase recovery failure. As expected, narrower-linewidth lasers exhibit improved phase stability and reduced variance, confirming the combined impact of pilot tone power and laser linewidth on phase recovery performance. These findings provide practical guidelines for CV-QKD receiver synchronization.