Optimal witnessing of the quantum Fisher information with few measurements

TL;DR

This paper presents a method to verify the quantum Fisher information of quantum states using only a few measurements, enabling efficient detection of metrologically useful entanglement in large systems.

Contribution

It introduces a tight lower bound estimation of quantum Fisher information from incomplete data, applicable to various experimental quantum states.

Findings

Successfully applied to photonic and ion trap experiments

Effective in detecting metrologically useful entanglement in large systems

Provides new insights into the relationship between entanglement and metrological usefulness

Abstract

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.