Minimum-error discrimination between three mirror-symmetric states

E. Andersson, S.M. Barnett, C.R. Gilson, K. 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
Pages (from-to)052308-1
Number of pages52307
JournalPhysical Review A
Issue number5
Publication statusPublished - 19 Apr 2002


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

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