  We use a recent numerical security proof approach to calculate tight secure
key rates in the presence of collective attacks for a continuous-variable (CV)
eight-state phase-shift keying (8PSK) protocol with heterodyne detection in the
asymptotic limit. The results are compared to achievable secure key rates of a
QPSK protocol obtained with the same security proof technique. Furthermore, we
investigate the influence of radial postselection on the secure key rate and
examine a recently suggested strategy to reduce the computational requirements
on the error-correction phase for four-state phase-shift-keying protocols.
Based on our investigations, we suggest different strategies to reduce the raw
key of 8PSK protocols significantly, only on the cost of a slightly lower
secure key rate. This can be used to lower the computational effort of the
error-correction phase, a known bottleneck in many practical implementations,
considerably.
