Quantum hacking of free-space continuous-variable quantum key distribution by using a machine-learning technique

The transmission coefficient of the free-space channel is fluctuating due to the occurrence of random fluctuations of the refractive index and noise. The Gaussian-modulated quantum states of light may degrade into a non-Gaussian mixture at a certain probability after being transmitted through the free-space channel. In such a situation, Eve can apply an entanglement-distillation attack to steal secret information without it being revealed if Alice and Bob regard the practical fluctuation losses as constant. However, the entanglement-distillation attack is available only when the transmitting states are a non-Gaussian mixture; otherwise, Eve will expose herself. Exploiting this loophole and considering the limitations of the attack, we enhance Eve's eavesdropping ability by integrating a machine-learning technique with the entanglement-distillation attack. With the help of convolutional neural network (CNN, one of the most popular machine leaning tools), Eve can choose the best opportunity to launch the entanglement-distillation attack. Therefore, Eve has a chance to bias the estimation of the parameters by improving the entanglement resource of the mixed states, which allows Eve to render the final keys shared between the legitimate parties insecure. Our proposed CNN-based entanglement-distillation attack does not require additional resources and can be implemented using simple means based on the present technologies.