  In this study, we analyze the efficiency of a protocol with discrete
modulation of continuous variable non-Gaussian states, the coherent states
having one photon added and then one photon subtracted (PASCS). We calculate
the secure key generation rate against collective attacks using the fact that
Eve's information can be bounded based on the protocol with Gaussian
modulation, which in turn is unconditionally secure. Our results for a
four-state protocol show that the PASCS always outperforms the equivalent
coherent states protocol under the same environmental conditions.
Interestingly, we find that for the protocol using discrete-modulated PASCS,
the noisier the line, the better will be its performance compared to the
protocol using coherent states. Thus, our proposal proves to be advantageous
for performing quantum key distribution in non-ideal situations.
