Detecting large quantum Fisher information with finite measurement precision

TL;DR

This paper presents an experimentally feasible method to estimate lower bounds on quantum Fisher information using finite measurement precision, enhancing detection of multipartite entanglement and quantum metrological usefulness.

Contribution

The authors introduce a protocol that improves lower bounds on QFI by incorporating an additional operation, applicable to current spin-squeezing experiments and linked to Leggett-Garg inequalities.

Findings

The protocol significantly increases QFI lower bounds in spin-squeezing experiments.

Large QFI is necessary for violating Leggett-Garg inequalities with coarse measurements.

The method is experimentally accessible and enhances quantum metrology capabilities.

Abstract

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.