  We study the robustness of quantum key distribution protocols using discrete
or continuous variables to the channel noise. We introduce the model of such
noise based on coupling of the signal to a thermal reservoir, typical for
continuous-variable quantum key distribution, to the discrete-variable case.
Then we perform a comparison of the bounds on the tolerable channel noise
between these two kinds of protocols using the same noise parametrization, in
the case of implementation which is perfect otherwise. Obtained results show
that continuous-variable protocols can exhibit similar robustness to the
channel noise when the transmittance of the channel is relatively high.
However, for strong loss discrete-variable protocols are superior and can
overcome even the infinite-squeezing continuous-variable protocol while using
limited nonclassical resources. The requirement on the probability of a
single-photon production which would have to be fulfilled by a practical source
of photons in order to demonstrate such superiority is feasible thanks to the
recent rapid development in this field.
