Minimum-error discrimination between three mirror-symmetric states

Erika Andersson, Stephen M. Barnett, Claire R. Gilson, Kieran Hunter

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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.
Original languageEnglish
Article number52307
Number of pages4
JournalPhysical Review A
Issue number5
Publication statusPublished - 19 Apr 2002


  • quantum physics
  • quantum states
  • mirror symmetry
  • optics
  • photonics

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