  Here we report the performance of a discrete modulated Continuous Variable
Quantum Key Distribution protocol based on eight and sixteen state optimal
Amplitude Phase Keying constellations with pure loss quantum channel
transmission. Our constellations use the same amplitudes and state probability
as in an optimal four-state unidimensional constellation model and apply
amplitude/phase modulation to the quadratures of coherent states. We compare
the obtained results with the performance of conventional $m$-PSK and $m$-APK
constellations. The results presented show that protocols that use the proposed
constellations outperform the ones based on conventional constellations in both
secret key rate and link distance. In special, our protocol is able to
accomplish viable SKR's in low transmittance regime, $\tau<0.2$.
