  We propose an experimentally accessible scheme to determine lower bounds on
the quantum Fisher information (QFI), which ascertains multipartite
entanglement or usefulness for quantum metrology. The scheme is based on
comparing the measurement statistics of a state before and after a small
unitary rotation. We argue that, in general, limited resolution of collective
observables prevents the detection of large QFI. This can be overcome by
performing an additional operation prior to the measurement. We illustrate the
power of this protocol for present-day spin-squeezing experiments, where the
same operation used for the preparation of the initial spin-squeezed state
improves the lower bound on the QFI by two orders of magnitude. We also
establish a connection to Leggett-Garg inequalities. We show how to simulate a
variant of the inequalities with our protocol and demonstrate that a large QFI
is necessary for their violation with coarse-grained detectors.
