  The sensitivity in optical interferometry is strongly affected by losses
during the signal propagation or at the detection stage. The optimal quantum
states of the probing signals in the presence of loss were recently found.
However, in many cases of practical interest, their associated accuracy is
worse than the one obtainable without employing quantum resources (e.g.
entanglement and squeezing) but neglecting the detector's loss. Here we detail
an experiment that can reach the latter even in the presence of imperfect
detectors: it employs a phase-sensitive amplification of the signals after the
phase sensing, before the detection. We experimentally demonstrated the
feasibility of a phase estimation experiment able to reach its optimal working
regime. Since our method uses coherent states as input signals, it is a
practical technique that can be used for high-sensitivity interferometry and,
in contrast to the optimal strategies, does not require one to have an exact
characterization of the loss beforehand.
