  We address the experimental determination of entropic quantum discord for
systems made of a pair of polarization qubits. We compare results from full and
partial tomography and found that the two determinations are statistically
compatible, with partial tomography leading to a smaller value of discord for
depolarized states. Despite the fact that our states are well described, in
terms of fidelity, by families of depolarized or phase-damped states, their
entropic discord may be largely different from that predicted for these classes
of states, such that no reliable estimation procedure beyond tomography may be
effectively implemented. Our results, together with the lack of an analytic
formula for the entropic discord of a generic two-qubit state, demonstrate that
the estimation of quantum discord is an intrinsically noisy procedure. Besides,
we question the use of fidelity as a figure of merit to assess quantum
correlations.
