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We propose an experimentally accessible scheme to determine lower bounds onthe quantum Fisher information (QFI), which ascertains multipartiteentanglement or usefulness for quantum metrology. The scheme is based oncomparing the measurement statistics of a state before and after a smallunitary rotation. We argue that, in general, limited resolution of collectiveobservables prevents the detection of large QFI. This can be overcome byperforming an additional operation prior to the measurement. We illustrate thepower of this protocol for present-day spin-squeezing experiments, where thesame operation used for the preparation of the initial spin-squeezed stateimproves the lower bound on the QFI by two orders of magnitude. We alsoestablish a connection to Leggett-Garg inequalities. We show how to simulate avariant of the inequalities with our protocol and demonstrate that a large QFIis necessary for their violation with coarse-grained detectors.

Detecting large quantum Fisher information with finite measurement precision