  We propose a long-distance continuous-variable quantum key distribution
(CVQKD) with four-state protocol using non-Gaussian state-discrimination
detection. A photon subtraction operation, which is deployed at the
transmitter, is used for splitting the signal required for generating the
non-Gaussian operation to lengthen the maximum transmission distance of CVQKD.
Whereby an improved state-discrimination detector, which can be deemed as an
optimized quantum measurement that allows the discrimination of nonorthogonal
coherent states beating the standard quantum limit, is applied at the receiver
to codetermine the measurement result with conventional coherent detector. By
tactfully exploiting multiplexing technique, the resulting signals can be
simultaneously transmitted through an untrusted quantum channel, and
subsequently sent to the state-discrimination detector and coherent detector
respectively. Security analysis shows that the proposed scheme can lengthen the
maximum transmission distance up to hundreds of kilometers. Furthermore, by
taking finite-size effect and composable security into account we obtain the
tightest bound of the secure distance, which is more practical than that
obtained in the asymptotic limit.
