Minimum-error discrimination among mirror-symmetric mixed quantum states

We provide an exact solution of finding the optimum measurement strategy for distinguishing three mixed quantum states with mirror symmetry. The signal states reside in two-dimensional Hilbert space. By mirror symmetry, two of the three states have the same prior probabilities and transform into each other under the mirror symmetry. We find that the optimum measurement strategy may consist of three, two, or a single nonzero probability operator measure elements depending upon the prior probabilities of the quantum signals.