  We evaluate the performance of coherent frequency-shift keying (CFSK)
alphabets for communication on quantum channels. We show that, contrarily to
what previously thought, the square-root-measurement (SRM) is sub-optimal for
discriminating CFSK states. Furthermore, we compute the maximum information
transmission rate of the CFSK alphabet, observing that it employs at least as
many frequency modes as the signal states, and compare it with standard
phase-shift-keying. Finally, we introduce a discretized CFSK alphabet with
higher mode-efficiency, exhibiting comparable error-probability performance
with respect to CFSK and better rate performance. Our results suggest the
existence of a tradeoff between the CFSK reduced error-probability and its mode
efficiency.
