  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 communicating through the medium
of an untrusted relay. We perform a security analysis that allows for general
transmissivity and thermal noise variance of each link, in which we assume an
eavesdropper performs a collective attack and controls the excess thermal noise
in the channels. The introduction of post-selection enables the parties to
sustain a secret key rate over distances exceeding those of existing CV MDI
protocols. In the worst-case scenario in which the relay is positioned
equidistant between them, we find that the parties may communicate securely
over a range of 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.
