Witnessing Spin-Orbital Entanglement using Resonant Inelastic X-Ray Scattering

TL;DR

This paper introduces a new method using resonant inelastic x-ray scattering (RIXS) to detect and quantify spin-orbital entanglement in materials by constructing a Hermitian generator from spectra and computing the quantum Fisher information.

Contribution

We develop a protocol for experimentally detecting spin--orbital entanglement via RIXS by constructing a Hermitian generator and calculating the quantum Fisher information, including realistic measurement limitations.

Findings

The protocol enables quantification of spin--orbital entanglement in materials.

The method provides upper bounds for $k$-producible states as entanglement witnesses.

Extended framework accounts for experimental measurement limitations.

Abstract

Entanglement plays a central role in quantum technologies, yet its characterization and control in materials remain challenging. Recent developments in spectrum-based entanglement witnesses have enabled new strategies for quantifying many-body entanglement in macroscopic materials. Here, we develop a protocol for detecting spin--orbital entanglement using experiment-accessible resonant inelastic x-ray scattering (RIXS). Central to our approach is the construction of a Hermitian generator from experimentally measurable spectra, which allows us to compute the quantum Fisher information (QFI) available in spin--orbital systems. The resulting QFI provides upper bounds for $k$-producible states and thus serves as a robust witness of spin--orbital entanglement. To account for realistic experimental limitations, we further extend our framework to include relaxed QFI bounds applicable to measurements lacking full polarization resolution.