Verifying the metrological usefulness of Dicke states with collective measurements

We present a method to verify the metrological usefulness of noisy Dicke states with only a few collective measurements, without the need for a direct measurement of the sensitivity. Our method determines the usefulness of the state for estimating the angle of rotation based on only the measurement of the total spin of the ensemble, which is the most relevant case for metrology with many-particle systems. We apply our method to recent experimental results with Dicke states.