  Injecting a non-Gaussian (Fock or Shr\"odinger cat) quantum state into the
dark port of a two-arm interferometer and a strong classical light into the
bright one, it is possible, in principle, to detect a given phase shift
unambiguously using the orthogonality between the original and displaced in the
interferometer non-Gaussian states.
  The optical losses degrade the sensitivity, introducing the finite "false
positive" and "false negative" detection errors. However, using the
state-of-art photodetectors, it is still possible to obtain better detection
fidelity than in the case of Gaussian quantum states.
