Finite-size analysis of eight-state continuous-variable quantum key distribution with the linear optics cloning machine

We propose a method to improve the secret key rate of an eight-state continuous-variable quantum key distribution (CVQKD) by using a linear optics cloning machine (LOCM). In the proposed scheme, an LOCM is exploited to compensate for the imperfections of Bob's apparatus, so that the generated secret key rate of the eight-state protocol could be well enhanced. We investigate the security of our proposed protocol in a finite-size scenario so as to further approach the practical value of a secret key rate. Numeric simulation shows that the LOCM with reasonable tuning gain λ and transmittance τ can effectively improve the secret key rate of eight-state CVQKD in both an asymptotic limit and a finite-size regime. Furthermore, we obtain the tightest bound of the secure distance by taking the finite-size effect into account, which is more practical than that obtained in the asymptotic limit.