The tracking and compensation of phase noise is critical to reducing excess noise for continuous variable quantum key distribution schemes. This work demonstrates the effectiveness of unscented Kalman filter for phase noise compensation.
Quantum key distribution (QKD) enables information-theoretic-secure secret key exchange thanks to the laws of quantum mechanics. Since it can easily be incorporated into existing telecom networks, continuous-variable QKD (CV QKD) using coherent states and coherent detection has recently emerged as a promising candidate. However, the secret key rate and link distance in CV QKD systems are still limited by the imperfections of used components. In this work, through simulations, we study the use of different digital filtering techniques for optical phase recovery, aided by pilot symbols, to mitigate the phase noise induced by the coherent mixing of two free-running lasers in a CV QKD system. Moving average, Butterworth and unscented Kalman filters are evaluated for different phase drift conditions. Results show that phase recovery from small amplitude pilot symbols, along with further digital filtering, can considerably reduce phase noise and measurement error, while increasing the secret key rate and link distance of the CV QKD system.
The continuous-variable quantum key distribution with a local local-oscillator is extremely sensitive to the phase compensation noise caused by the inaccurate reference phase estimation. In order to overcome the influence of slow drift caused by the residual optical frequency difference, we utilize a vector Kalman filter to estimate and track the reference phase from pilots. The fast drift and slow drift are taken into account in the variation of the reference phase, so that phase estimation becomes more accurate than the conventional scalar Kalman filter. The mean square error of reference phase estimation is deduced theoretically, and the specified frame is designed to estimate the phase noise variance in real time. In simulations, the performances involving of the estimation accuracy, the actual excess noise and the secret key rate are compared between with four different phase estimation methods. The simulation results show that the vector Kalman filter is superior to the other methods, even though under a serious phase noise and a large optical frequency difference.
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.
The traditional phase compensation method in CVQKD (continuous variable quantum key distribution) usually assumes that the phase drift within a frame is constant. However, in reality, there are usually small phase drifts within a frame, especially in free space. Unperfect compensation of phase drifts can introduce additional phase noise, which can reduce key rate and transmission distance. To address this issue, we propose a two-stage phase compensation scheme that inserts different length phase drift compensation blocks to not only compensate for the average phase drift of a frame but also to compensate for the internal phase drift fluctuations within the frame. This enables more accurate phase drift compensation, particularly useful for scenarios with large and fast phase drift fluctuations.
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.
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.