  Noise affects the performance of quantum technologies, hence the importance
of elaborating operative figures of merit that can capture its impact in exact
terms. In quantum metrology, the introduction of the Fisher information
measurement noise susceptibility now allows to quantify the robustness of
measurement for single-parameter estimation. Here we extend this notion to the
multiparameter quantum estimation scenario. We provide its mathematical
definition in the form of a semidefinite program. Although a closed formula
could not be found, we further derive an upper and a lower bound to the
susceptibility. We then apply these techniques to two paradigmatic examples of
multiparameter estimation: the joint estimation of phase and phase-diffusion
and the estimation of the different parameters describing the incoherent
mixture of optical point sources. Our figure of merit provides clear
indications on conditions allowing or hampering robustness of multiparameter
measurements.
