  In quantum information processing, {using a receiver device to differentiate
between two nonorthogonal states leads to a quantum error probability. The
minimum possible error is} known as the Helstrom bound. In this work we study
and compare quantum limits for states which generalize the Glauber-Sudarshan
coherent states, like non-linear, Perelomov, Barut-Girardello, and (modified)
Susskind-Glogower coherent states. For some of these, we show that the Helstrom
bound can be significantly lowered and even vanish in specific regimes.
