We study the impact of the finite-size effect on the continuous-variable
measurement-device-independent quantum key distribution (CV-MDI QKD) protocol,
mainly considering the finite-size effect on the parameter estimation
procedure. The central-limit theorem and maximum likelihood estimation theorem
are used to estimate the parameters. We also analyze the relationship between
the number of exchanged signals and the optimal modulation variance in the
protocol. It is proved that when Charlie's position is close to Bob, the CV-MDI
QKD protocol has the farthest transmission distance in the finite-size
scenario. Finally, we discuss the impact of finite-size effects related to the
practical detection in the CV-MDI QKD protocol. The overall results indicate
that the finite-size effect has a great influence on the secret key rate of the
CV-MDI QKD protocol and should not be ignored.Comment: 9 pages, 9 figure
