Continuous-variable quantum key distribution with discretized modulations in the strong noise regime

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 study 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 a strong signal, QKD is impossible. In this case, from the perspective of an efficient eavesdropper, the ensemble of transmitted states is effectively classical and the amount of leaked information is limited only by the entropy of the distribution of transmitted states, while the mutual information between the legitimate parties is also subject to such limiting factors as detection and reconciliation efficiencies. 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, for which we obtain an explicit form of the condition where the secret key can be generated in the asymptotic limit. When the noise is weak, however, QKD may become possible only when the signal strength exceeds some critical value.