We’re excited to share our latest work, just published in Physical Review B and selected as an Editor’s Suggestion: Quantum entanglement and quantum geometry measured with inelastic x-ray scattering

In this study, we explore how quantum geometry and entanglement—usually thought of as purely theoretical concepts—can be directly measured in scattering experiments. We demonstrate a connection between the quantum Fisher information (QFI) and quantum weight, a measure of wavefunction geometry in insulators, and validate this relationship using inelastic x-ray scattering (IXS) data from LiF.

Both the QFI and the quantum weight are related to a material’s density-density response function. The QFI captures how rapidly the equilibrium density matrix responds to an external perturbation, offering a measure of the system’s intrinsic sensitivity. The quantum weight, on the other hand, is related to wave function geometry, reflecting bounds on fluctuation and localization, and in the limit of small momentum transfer and low temperature, can also be experimentally accessed via the density-density response function.

Our experimental results reveal that the quantum weight in LiF lies close to its theoretical upper bound. This suggests that, while LiF is a strongly localized ionic insulator, its electrons are nearly as delocalized, geometrically as quantum mechanics allows for a system with its material parameters.

This work bridges condensed matter and quantum information concepts, and also demonstrates a general strategy for experimentally accessing entanglement and quantum geometry in many-body systems where the charge density is measured.