  A sequential measurement of two non-commuting quantum observables results in
a joint probability distribution for all output combinations that can be
explained in terms of an initial joint quasi-probability of the non-commuting
observables, modified by the resolution errors and back-action of the initial
measurement. Here, we show that the error statistics of a sequential
measurement of photon polarization performed at different measurement strengths
can be described consistently by an imaginary correlation between the
statistics of resolution and back-action. The experimental setup was designed
to realize variable strength measurements with well-controlled imaginary
correlation between the statistical errors caused by the initial measurement of
diagonal polarizations, followed by a precise measurement of the
horizontal/vertical polarization. We perform the experimental characterization
of an elliptically polarized input state and show that the same complex joint
probability distribution is obtained at any measurement strength.
