Finite-size analysis of continuous-variable quantum key distribution with entanglement in the middle

Continuous-variable quantum key distribution(CVQKD) protocols with entanglement in the middle(EM) enable long maximal transmission distances for quantum communications. For the security analysis of the protocols, it is usually assumed that Eve performs collective Gaussian attacks and there is a lack of finite-size analysis of the protocols. However,in this paper we consider the finite-size regime of the EM-based CVQKD protocols by exposing the protocol to collective attacks and coherent attacks. We differentiate between the collective attacks and the coherent attacks while comparing asymptotic key rate and the key rate in the finite-size scenarios. Moreover, both symmetric and asymmetric configurations are collated in a contrastive analysis. As expected, the derived results in the finite-size scenarios are less useful than those acquired in the asymptotic regime. Nevertheless, we find that CVQKD with entanglement in the middle is capable of providing fully secure secret keys taking the finite-size effects into account with transmission distances of more than 30 km.