Optimal witnessing of the quantum Fisher information with few measurements

We show how to verify the metrological usefulness of quantum states based on few measurements. In particular, we estimate the quantum Fisher information as a figure of merit of metrological usefulness. Our approach is optimal since it gives a tight lower bound on the quantum Fisher information for the given incomplete information. We apply our method to the results of various multi-particle quantum states prepared in experiments with photons and trapped ions, as well as to spin-squeezed states and Dicke states realized in cold gases.