# Relating out-of-time-order correlations to entanglement via multiple-quantum coherences

## TL;DR

This paper demonstrates that multiple-quantum coherence spectra, a type of out-of-time-order correlation, can serve as an experimentally accessible entanglement witness, linking quantum chaos, entanglement, and fundamental physics.

## Contribution

It establishes a formal connection between multiple-quantum coherences and entanglement, enabling experimental probing of multiparticle entanglement via OTOCs.

## Key findings

- Multiple-quantum coherences act as entanglement witnesses.
- OTOCs can directly probe multiparticle entanglement.
- Results suggest a link between entanglement, thermodynamics, and quantum gravity.

## Abstract

Out-of-time-order correlations (OTOCs) characterize the scrambling, or delocalization, of quantum information over all the degrees of freedom of a system and thus have been proposed as a proxy for chaos in quantum systems. Recent experimental progress in measuring OTOCs calls for a more thorough understanding of how these quantities characterize complex quantum systems, most importantly in terms of the buildup of entanglement. Although a connection between OTOCs and entanglement entropy has been derived, the latter only quantifies entanglement in pure systems and is hard to access experimentally. In this work, we formally demonstrate that the multiple-quantum coherence spectra, a specific family of OTOCs well known in NMR, can be used as an entanglement witness and as a direct probe of multiparticle entanglement. Our results open a path to experimentally testing the fascinating idea that entanglement is the underlying glue that links thermodynamics, statistical mechanics, and quantum gravity.