  Using the known necessary and sufficient conditions for minimum error
discrimination (MED), first it is shown that a Helstrom family of ensembles is
equivalent to these conditions and then by a convex combination of the initial
states (the states which we try to discriminate them) and the corresponding
conjugate states, a more suitable and convenient form for the MED conditions is
extracted, so that optimal set of measurements and corresponding optimal
success probability of discrimination can be determined. Then, using the
introduced identity, MED between N similarity transformed equiprobable quantum
states is investigated. As a special case, MED between the so called group
covariant or symmetric states is considered.
