  A measurement strategy is developed for a new kind of hypothesis testing. It
assigns, with minimum probability of error, the state of a quantum system to
one or the other of two complementary subsets of a set of N given
non-orthogonal quantum states occurring with given a priori probabilities. A
general analytical solution is obtained for N states that are restricted to a
two-dimensional subspace of the Hilbert space of the system. The result for the
special case of three arbitrary but linearly dependent states is applied to a
variety of sets of three states that are symmetric and equally probable. It is
found that, in this case, the minimum error probability for distinguishing one
of the states from the other two is only about half as large as the minimum
error probability for distinguishing all three states individually.
