Abstract We propose a novel scheme for discretely-modulated continuous-variable quantum key distribution (CVQKD) using machine learning technologies, which called multi-label learning-based CVQKD (ML-CVQKD). In particular, the proposed scheme divides the whole quantum system into state learning process and state prediction process. The former is used for training and estimating classifier, and the latter is used for generating final secret key. Meanwhile, a multi-label classification algorithm (MLCA) is also designed as an embedded classifier for distinguishing coherent state. Feature extraction for coherent state and related machine learning-based metrics for the quantum classifier are successively suggested. Security analysis based on the linear bosonic channel assumption shows that MLCA-embedded ML-CVQKD outperforms other existing discretely-modulated CVQKD protocols, such as four-state protocol and eight-state protocol, as well as the original Gaussian-modulated CVQKD protocol, and it will be further enhanced with the increase of modulation variance.
Continuous-variable quantum key distribution (CV-QKD) with discrete modulation has received widespread attentions because of its experimental simplicity, lower-cost implementation and ease to multiplex with classical optical communication. Recently, some inspiring numerical methods have been applied to analyse the security of discrete-modulated CV-QKD against collective attacks, which promises to obtain considerable key rate over one hundred kilometers of fiber distance. However, numerical methods require up to ten minutes to calculate a secure key rate one time using a high-performance personal computer, which means that extracting the real-time secure key rate is impossible for discrete-modulated CV-QKD system. Here, we present a neural network model to quickly predict the secure key rate of homodyne detection discrete-modulated CV-QKD with good accuracy based on experimental parameters and experimental results. With the excess noise of about
0.01, the speed of our method is improved by about seven orders of magnitude compared to that of the conventional numerical method. Our method can be extended to quickly solve complex security key rate calculation of a variety of other unstructured quantum key distribution protocols.