The performance of local local oscillator-based continuous-variable quantum key distribution (LLO-CVQKD) systems is critically limited by phase recovery accuracy. To address the phase mismatch between independently operated lasers at the transmitter and receiver, this work proposes a multi-pilot scheme integrated with advanced digital filtering for optimized phase estimation. Through systematic comparisons of the rectangular filter, Savitzky-Golay filter, and Wiener filter, experimental results confirm that Wiener filtering has superior noise suppression capabilities based on multiple frequency pilot-tones. Implemented under the Gaussian-modulated coherent state (GMCS) protocol, our findings reveal that dual-pilot, four-pilot, and eight-pilot configurations all enhance phase recovery precision compared to single-pilot approaches, with the dual-pilot scheme achieving optimal balance between system complexity and performance. In a 20 km fiber link with a 1 GHz system repetition rate and a 2.83 SNU modulation variance, the dual-pilot Wiener-filtered configuration achieves an asymptotic secret key rate of almost 80 Mbps, establishing an innovative approach for practical LLO-CVQKD phase recovery.
The performance of local local oscillator-based continuous-variable quantum key distribution (LLO-CVQKD) systems is critically limited by phase recovery accuracy. To address the phase mismatch between independently operated lasers at the transmitter and receiver, this work proposes a multi-pilot scheme integrated with advanced digital filtering for optimized phase estimation. Through systematic comparisons of the rectangular filter, Savitzky-Golay filter, and Wiener filter, experimental results confirm that Wiener filtering has superior noise suppression capabilities based on multiple frequency pilot-tones. Implemented under the Gaussian-modulated coherent state (GMCS) protocol, our findings reveal that dual-pilot, four-pilot, and eight-pilot configurations all enhance phase recovery precision compared to single-pilot approaches, with the dual-pilot scheme achieving optimal balance between system complexity and performance. In a 20 km fiber link with a 1 GHz system repetition rate and a 2.83 SNU modulation variance, the dual-pilot Wiener-filtered configuration achieves an asymptotic secret key rate of almost 80 Mbps, establishing an innovative approach for practical LLO-CVQKD phase recovery.
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.
A high-speed Gaussian-modulated continuous-variable quantum key distribution (CVQKD) with a local local oscillator (LLO) is experimentally demonstrated based on pilot-tone-assisted phase compensation. In the proposed scheme, the frequency-multiplexing and polarization-multiplexing techniques are used for the separate transmission and heterodyne detection between quantum signal and pilot tone, guaranteeing no crosstalk from strong pilot tone to weak quantum signal and different detection requirements of low-noise for quantum signal and high-saturation limitation for pilot tone. Moreover, compared with the conventional CVQKD based on homodyne detection, the proposed LLO-CVQKD scheme can measure X and P quadrature simultaneously using heterodyne detection without need of extra random basis selection. Besides, the phase noise, which contains the fast-drift phase noise due to the relative phase of two independent lasers and the slow-drift phase noise introduced by quantum channel disturbance, has been compensated experimentally in real time, so that a low level of excess noise with a 25 km optical fiber channel (with 5 dB loss) is obtained for the achievable secure key rate of 7.04 Mbps in the asymptotic regime and 1.85 Mbps under the finite-size block of 107.
We experimentally demonstrate a 25 MHz repetition rate pilot-tone-assisted Gaussian-modulated continuous-variable quantum key distribution (CVQKD) with a local local oscillator (LLO) by employing the frequency-multiplexing and polarization-multiplexing techniques. In the proposed LLO-CVQKD system, the strong pilot tone and weak quantum signal can be separated in different frequency and polarization domain for avoiding the crosstalk between them and guaranteeing different detection requirements of low-noise for quantum signal and high-saturation limitation for pilot tone. Moreover, the dominant phase noise over 25 km optical fiber channel can be compensated in real time for supporting high secure key rate of 1.61 Mbps in the asymptotic regime.
Accurately estimating phase is crucial in continuous-variable quantum key distribution systems, directly impacting the final secret key rate. In previous systems that utilize the local local oscillator, phase estimation is closely tied to the amplitude and signal-to-noise ratio (SNR) of the pilot signal. As SNR decreases, so does the accuracy of phase estimation, leading to increased excess noise and a potential loss of the system's secret key rate. The SNR of the pilot signal is constrained by the optical source power, which tends to approach 0 dB, particularly over long distances. Enhancing the accuracy of phase estimation under conditions of low SNR for pilot signals is highly challenging, especially in long-distance quantum key distribution. Our paper proposes two digital filter methods: the unscented Kalman filtering (UKF) and the Savitzky-Golay filtering (SGF) for phase estimation, which effectively mitigates the effects of additive noise. The approach applies to digital systems and therefore holds particular advantages in systems based on discrete-modulation (DM) protocols. Through simulations and practical implementation based on DM protocols, we find that the digital filter scheme is capable of accurately estimating phase, especially in scenarios with low SNR of the pilot signal. The conventional method fails to achieve an effective secret key rate, whereas the digital-filter-based scheme achieves a secret key rate of almost 30 kbps over a 20 km fiber link with a repetition frequency of 5 MHz under conditions where the SNR of the pilot signal is around 0 dB.
Local local oscillator (LLO) continuous-variable quantum key distribution (CVQKD) systems have gained prominence due to their security advantages with LO generated locally. However, the nonsynchronization of two lasers leads to phase drift, a detrimental phenomenon that restricts excess noise suppression. Prevailing solutions, such as pilot-multiplexing schemes, offer better recovery results than pilot-sequential schemes, but at the expense of increased system complexity and demanding technical requirements. In this work, we introduce an innovative carrier-recovery strategy employing the long-short-term memory (LSTM) neural network, aiming to optimize the recovery performance in the simple self-referenced CVQKD systems with the pilot-sequential scheme. Through temporal modeling, the LSTM network proficiently predicts and compensates for the rapid phase drifts. Experimental validations conducted in both fiber and free-space channels underscore the effectiveness of our method for carrier recovery. In practical CVQKD experiments, our LSTM-based approach yields a near 50% reduction in excess noise, leading to a significant increase in secret key rates when compared with the traditional pilot-sequential method. The simplicity of hardware and operation positions our scheme as a superior alternative for current mainstream pilot-multiplexing CVQKD systems, particularly appealing for on-chip implementation and satellite-to-ground quantum communication applications.
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.