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Minimum-error discrimination between three mirror-symmetric states

Andersson, E. and Barnett, S.M. and Gilson, C.R. and Hunter, K. (2002) Minimum-error discrimination between three mirror-symmetric states. Physical Review A, 65 (5). 052308-1. ISSN 1094-1622

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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.