Long-distance continuous-variable measurement-device-independent quantum key distribution with post-selection

We introduce a robust scheme for long-distance continuous-variable (CV) measurement-device-independent (MDI) quantum key distribution (QKD) in which we employ post-selection between distant parties separated by an untrusted relay. We perform a security analysis that allows for general distances between the parties and the thermal noise on each link. We assume an eavesdropper performs a collective attack and controls the excess thermal noise in the channels. Our introduction of post-selection allows the parties to sustain a high secret key rate which exceeds any existing CV MDI protocol. In the worst-case scenario in which the relay is positioned equidistant between the communicating parties, we find secure communication is possible over distances exceeding 14 km in standard optical fiber. Our protocol helps to overcome the rate-distance limitations of previously proposed CV MDI protocols while maintaining many of their advantages.