Improved Four-state Continuous-variable Quantum Key Distribution with Long Secure Distance

The four-state continuous-variable quantum key distribution (CVQKD) protocol has a long practical secure distance \cite{Leverrier_PRL_2009}, while it has the difficulty of parameter estimation. We propose an improved four-state protocol, where the covariance matrix can be estimated from experimental data without using the linear channel assumption, and thus ensuring its unconditional security in the asymptotical limit. Our new scheme keeps the advantages of high reconciliation efficiency and long secure distance of the four-state protocol, and it can be implemented under current technology.