  We have experimentally evaluated the non-classical relation between
measurement errors in a joint measurement of two non-commuting polarizations by
using entangled photon pairs as a probe. The joint measurement was realized by
filtering polarization directions that are sensitive to both of the two target
polarizations and the same filtering procedures were applied independently to
the two photons of an entangled pair. Since the statistically independent
measurement errors of two identical measurements performed on entangled pairs
will reduce an overall visibility of the correlation by the square of the local
visibilities, the squared visibilities of the local measurements can be
obtained directly from the measurement data. We apply this method to determine
the visibility of the correlation between the products of the two non-commuting
polarizations, a characteristic of the measurement errors that can not be
obtained locally since there is no self-adjoint operator that describes this
product of measurement outcomes as a single photon observable. The experimental
results clearly show that the square of the product visibility is negative,
indicating the non-classical nature of the statistical relation between the
measurement errors of non-commuting polarizations.
