  Distinguishing assigned quantum states with assigned probabilities via
quantum measurements is a crucial problem for the transmission of classical
information through quantum channels. Measurement operators maximizing the
probability of correct discrimination have been characterized by Helstrom,
Holevo and Yuen since 1970's. On the other hand, closed--form solutions are
available only for particular situations enjoying high degrees of symmetry. As
a suboptimal solution to the problem, measurement operators, directly
determined from states and probabilities and known as square root measurements
(SRM), were introduced by Hausladen and Wootters. These operators were also
recognized to be optimal for pure states equipped with geometrical uniform
symmetry (GUS). In this paper we discuss the optimality of the SRM and find
necessary and sufficient conditions in order that SRM maximize the correct
decision probabilities for set of states formed by several constellations of
GUS states. The results are applied to some specific examples concerning double
constellations of quantum phase shift keying (PSK) and pulse position
modulation (PPM) states, with possible applications to practical systems of
quantum communications.
