  We present the results of generalized measurements of optical polarization
designed to provide one of three or four distinct outcomes. This has allowed us
to discriminate between nonorthogonal polarization states with an error
probability that is close to the minimum allowed by quantum theory. Employing
these optimal detection strategies on sets of three (trine) or four (tetrad)
equiprobable symmetric nonorthogonal polarization states, we obtain a mutual
information that exceeds the maximum value attainable using conventional (von
Neumann) polarization measurements.
