Leggett-Garg Inequality Violations Bound Quantum Fisher Information

TL;DR

This paper establishes that violations of the Leggett-Garg inequality provide a quantitative lower bound on quantum Fisher information, linking foundational quantum tests to practical quantum sensing and entanglement detection.

Contribution

It demonstrates that Leggett-Garg violations can serve as a quantitative witness of quantum sensitivity and multipartite entanglement in many-body systems.

Findings

Violations yield a lower bound on quantum Fisher information.

Leggett-Garg violations relate to spectral moments and susceptibilities.

Temporal correlations can witness many-body quantum coherence.

Abstract

We prove that a violation of a Leggett-Garg inequality for bounded observables in stationary pure states and thermal states yields a rigorous lower bound on the quantum Fisher information. This turns a qualitative foundations test of realism in quantum systems into a quantitative witness of useful quantum sensitivity and, in the collective setting, into a lower bound on multipartite entanglement depth in many-body systems. We further demonstrate that Leggett-Garg violations are constrained by the same spectral moments, susceptibilities, and $f$-sum-rule bounds that organize many-body response. Our results show that temporal correlations of a single collective observable can serve as an experimentally accessible witness of many-body quantum coherence, without requiring full state reconstruction.