  We investigate the performance of several continuous-variable quantum key
distribution protocols in the presence of fading channels. These are lossy
channels whose transmissivity changes according to a probability distribution.
This is typical in communication scenarios where remote parties are connected
by free-space links subject to atmospheric turbulence. In this work, we assume
the worst-case scenario where an eavesdropper has full control of a fast fading
process, so that she chooses the instantaneous transmissivity of a channel,
while the remote parties can only detect the mean statistical process. In our
study, we consider coherent-state protocols run in various configurations,
including the one-way switching protocol in reverse reconciliation, the
measurement-device-independent protocol in the symmetric configuration and a
three-party measurement-device-independent network. We show that, regardless of
the advantage given to the eavesdropper (full control of fading), these
protocols can still achieve high rates.
