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Minimum-error discrimination between three mirror-symmetric states

Erika Andersson·Stephen M. Barnett·Claire R. Gilson·Kieran Hunter
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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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Erika Andersson, Stephen M. Barnett, Claire R. Gilson, Kieran Hunter. 2002-01-17. Minimum-error discrimination between three mirror-symmetric states. https://doi.org/10.1103/physreva.65.052308

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