Continuous-variable quantum key distribution with extended Kalman filter assisted by recurrent neural networks for phase estimation

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.