Measuring multipartite entanglement via dynamic susceptibilities

TL;DR

This paper demonstrates that the quantum Fisher information, a measure of multipartite entanglement, can be experimentally accessed through dynamic susceptibilities in many-body quantum systems, linking entanglement to response functions near phase transitions.

Contribution

It introduces a method to measure multipartite entanglement via dynamic susceptibilities, connecting entanglement detection with experimentally accessible response functions.

Findings

Quantum Fisher information is measurable through dynamic susceptibility.

Multipartite entanglement diverges near quantum phase transitions.

Framework applied to quantum Ising models with experimental signatures in optical lattices.

Abstract

Entanglement plays a central role in our understanding of quantum many body physics, and is fundamental in characterising quantum phases and quantum phase transitions. Developing protocols to detect and quantify entanglement of many-particle quantum states is thus a key challenge for present experiments. Here, we show that the quantum Fisher information, representing a witness for genuinely multipartite entanglement, becomes measurable for thermal ensembles via the dynamic susceptibility, i.e., with resources readily available in present cold atomic gas and condensed-matter experiments. This moreover establishes a fundamental connection between multipartite entanglement and many-body correlations contained in response functions, with profound implications close to quantum phase transitions. There, the quantum Fisher information becomes universal, allowing us to identify strongly entangled phase transitions with a divergent multipartiteness of entanglement. We illustrate our framework using paradigmatic quantum Ising models, and point out potential signatures in optical-lattice experiments.