  The physics that governs quantum monitoring may involve other degrees of
freedom than the ones initialised and controlled for probing. In this context
we address the simultaneous estimation of phase and dephasing characterizing a
dispersive medium, and we explore the role of frequency correlations within a
photon pair generated via parametric down-conversion, when used as a probe for
the medium. We derive the ultimate quantum limits on the estimation of the two
parameters, by calculating the corresponding quantum Cram\'er-Rao bound; we
then consider a feasible estimation scheme, based on the measurement of Stokes
operators, and address its absolute performances in terms of the correlation
parameters, and, more fundamentally, of the role played by correlations in the
simultaneous achievability of the quantum Cram\'er-Rao bounds for each of the
two parameters.
