We show how to verify the metrological usefulness of quantum states based on
the expectation values of an arbitrarily chosen set of observables. In
particular, we estimate the quantum Fisher information as a figure of merit of
metrological usefulness. Our approach gives a tight lower bound on the quantum
Fisher information for the given incomplete information. We apply our method to
the results of various multiparticle quantum states prepared in experiments
with photons and trapped ions, as well as to spin-squeezed states and Dicke
states realized in cold gases. Our approach can be used for detecting and
quantifying metrologically useful entanglement in very large systems, based on
a few operator expectation values. We also gain new insights into the
difference between metrological useful multipartite entanglement and
entanglement in general.Comment: 14 pages including 7 figures, revtex4.1, v2:typos corrected,
published versio
