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We introduce a robust scheme for long-distance continuous-variable (CV)measurement-device-independent (MDI) quantum key distribution (QKD) in which weemploy post-selection between distant parties communicating through the mediumof an untrusted relay. We perform a security analysis that allows for generaltransmissivity and thermal noise variance of each link, in which we assume aneavesdropper performs a collective attack and controls the excess thermal noisein the channels. The introduction of post-selection enables the parties tosustain a secret key rate over distances exceeding those of existing CV MDIprotocols. In the worst-case scenario in which the relay is positionedequidistant between them, we find that the parties may communicate securelyover a range of 14 km in standard optical fiber. Our protocol helps to overcomethe rate-distance limitations of previously proposed CV MDI protocols whilemaintaining many of their advantages.

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