Minimum-error discrimination between three mirror-symmetric states
Erika Andersson, Stephen M. Barnett, Claire R. Gilson, Kieran Hunter
Abstract
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.
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