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.
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.
In local oscillator (LLO)-based continuous-variable quantum key distribution (CV-QKD), a difference between the linewidth values of two free-running lasers at Alice and Bob induces a phase drift noise. This work proposes a novel minimax filter-based phase tracking that aims to minimize the phase drift considering maximum residual phase error to achieve optimal phase estimation. Simulation results show that the minimax filter offers a lower phase estimation mean square error (MSE) value compared to the Kalman filter when worst-case phase drift error due to high linewidth difference or high measurement noise values are considered.
Continuous-variable quantum key distribution (CVQKD) with a real local oscillator (LO) is confronted with new security issues attributed to the reference pulses transmitted together with quantum signals over the insecure quantum channel. This paper proposes a method of phase attack on reference pulses of the CVQKD with real LOs. Under the phase attack, the phase drifts of reference pulses are manipulated by eavesdroppers so that the phase compensation error is increased. Consequently, the secret key rate is reduced because of the imperfect phase compensation for quantum signals. Based on the noise model of imperfect phase compensation, both the parameters of actual transmittance and actual excess noise are deduced from the phase compensation accuracy, and then they are compared with those estimated by training signals. The simulation results show that the secret key rate calculated from the theoretical parameters is consistent with the one estimated by training signals.
Excess noise induced by the phase drifts is a serious impairment for the continuous-variable quantum key distribution with locally generated local oscillator scheme, which is recently proposed to avoid the side channel attacks due to the transmitted local oscillator. Theoretical and experimental studies on the phase estimation have been widely reported, while two frequency-locked laser sources are indispensable to achieve quantum coherent detection. Moreover, the self-referenced phase estimation scheme requires to propagate the strong reference pulse through optical fiber, which opens a security loophole through the manipulation of the reference pulse amplitude. Based on the theoretical security and Bayes' theorem, we propose a phase estimation protocol, which does not require propagating the strong reference pulse for performing phase estimation. Compared to the other related work, the protocol can avoid the security problem caused by strong reference pulse. Moreover, this algorithm is an iterative progress for each of experiment to obtain the phase estimation and its uncertainty. We hope the proposed scheme could further promote the performance of continuous-variable quantum key distribution.
Abstract Although the continuous-variable quantum key distribution (CV-QKD) protocol based on a local local oscillator (LLO) can close all the security loopholes from the transmitted local oscillator (TLO), the phase noise caused by the inaccurate phase reference information limits the performance of the protocol. To reduce the residual phase noise, in this work, we propose a phase estimation and compensation method based on the temporal convolutional neural (TCN) model, where a part of phase information obtained by measuring pilot pulses is employed as the training data and input into the TCN module. With a trained TCN module, the subsequent phase drifts can be more accurately estimated, allowing for better phase compensation and lower phase noise. Numerical analysis shows that the proposed scheme can improve the transmission distance and the secret key rate of the LLO protocol.
In a practical continuous-variable quantum secret sharing system, the local oscillator transmitted via an insecure channel may be subjected to security threats due to various targeted attacks. To solve this problem, this paper proposes a continuous-variable quantum secret sharing scheme with local intrinsic oscillator, in which the intrinsic oscillator is generated locally at the trusted end without being sent by each user, thus completely plugging the relevant security loopholes. The scheme consists of three stages: preparation, where users generate Gaussian-modulated coherent states and reference signals; measurement, where the dealer performs heterodyne detection by using the local intrinsic oscillator and reference phases; post-processing, which involves parameter estimation, phase compensation, and secure key extraction. On this basis, Kalman filter (KF) is utilized to estimate the minimum mean square error for each reference phase separately, reducing the phase drift estimation error and suppressing the phase measurement noise. Phase compensation methods for scalar KF and vector KF are developed respectively, where scalar KF requires additional block averaging for slow phase drift, while vector KF simultaneously models fast and slow drifts, enabling one-step compensation with minimized estimation errors. The excess noise of the filtered system including modulation noise, phase noise, photon leakage noise, and ADC quantization noise is modeled, with KF reducing phase measurement noise via dynamic gain optimization. Security bound against eavesdroppers and dishonest users is derived. Numerical simulations under practical parameters demonstrate significant improvements: vector KF achieves a maximum transmission distance of 82.6 km (vs. 67.3 km for block averaging) and supports 33 users (vs. 22), with excess noise reduced by 40% at 60 km. The scheme’s robustness is further validated under varying reference signal amplitudes, showing stable performance even at lower levels, minimizing interference with quantum signals. These results highlight that the proposed scheme has significant advantages in terms of maximum transmission distance and maximum number of supported users, and has the potential to build adaptive KF algorithms for dynamic user scenarios and quantum machine learning integration.
Continuous-variable quantum key distribution with a real local oscillator (LO) has been extensively studied recently due to its security and simplicity. Making it operate automatically and resistant to channel interference is the key to further long-term system operation. To overcome the dynamic changes in the state of polarization (SOP) of quantum signal caused by the random birefringence effect in fiber, Kalman filter is employed to estimate the polarization misalignment, thereby achieving polarization demultiplexing at the data level, and ultimately recovering the quantum signal with the help of a two-step phase compensation. The signal transmission and processing is simulated, which verifies the SOP tracking ability and the immunity to the fast phase drift. A proof-of-principle experiment is also conducted, and results show that it can resist the interference of SOP rotation at 1 krad/s, and has the ability to distribute 8.4 kbps secret key rate within 20 km when only considering SOP tracking imperfection, confirming its feasibility under harsh channel conditions.