  We consider a general family of quantum key distribution (QKD) protocols
utilizing displaced thermal states with discretized modulations. Separating the
effects of the Gaussian channel and the non-Gaussian distribution, we have
studied the dependence of the secret key generation rate on the magnitude of
modulations (the strength of the modulated signal). We show that in the limit
of strong signal, QKD is impossible: from the perspective of an efficient
eavesdropper, the ensemble of transmitted states is effectively classical. This
constitutes a quantum correction to performance of finite-length QKD protocols.
We demonstrate that two regimes must be distinguished: weak and strong thermal
noise. In the case of strong noise, the security boundary is mostly determined
by the weak-signal limit. When the noise is weak, however, QKD may become
possible only when the signal strength exceeds some critical value.
