  A quantum measurement can be described by a set of matrices, one for each
possible outcome, which represents the positive operator-valued measure (POVM)
of the sensor. Efficient protocols of POVM extraction for arbitrary sensors are
required. We present the first experimental POVM reconstruction that takes
explicit advantage of a quantum resource, i.e., nonclassical correlations with
an ancillary state. A POVM of a photon-number-resolving detector is
reconstructed by using strong quantum correlations of twin beams generated by
parametric down-conversion. Our reconstruction method is more statistically
robust than POVM reconstruction methods that use classical input states.
