Does a large quantum Fisher information imply Bell correlations?

TL;DR

This paper investigates whether large quantum Fisher information in multipartite entangled states necessarily indicates Bell correlations, providing specific examples and discussing the open question of their general relationship.

Contribution

It presents evidence linking high QFI to Bell inequality violations through two examples, advancing understanding of quantum correlations and metrological advantages.

Findings

Bell inequality violation occurs only with large QFI in spin-squeezed states

Relaxing QFI bounds reveals the Mermin Bell inequality as a special case

A general link between QFI and Bell correlations remains unproven

Abstract

The quantum Fisher information (QFI) of certain multipartite entangled quantum states is larger than what is reachable by separable states, providing a metrological advantage. Are these nonclassical correlations strong enough to potentially violate a Bell inequality? Here, we present evidence from two examples. First, we discuss a Bell inequality designed for spin-squeezed states which is violated only by quantum states with a large QFI. Second, we relax a well-known lower bound on the QFI to find the Mermin Bell inequality as a special case. However, a fully general link between QFI and Bell correlations is still open.