Minimum-error discrimination between three mirror-symmetric states
  We present the optimal measurement strategy for distinguishing between three quantum states exhibiting a mirror symmetry. The three states live in a two-dimensional Hilbert space, and are thus overcomplete. By mirror symmetry we understand that the transformation {|+> -> |+>, |-> -> -|->} leaves the set of states invariant. The obtained measurement strategy minimizes the error probability. An experimental realization for polarized photons, realizable with current technology, is suggested. 
Erika Andersson, Stephen M. Barnett, Claire R. Gilson, and Kieran   Hunter