Entanglement Witness for Indistinguishable Electrons using Solid-State Spectroscopy

TL;DR

This paper presents a novel method to detect and quantify entanglement among indistinguishable electrons in quantum materials using resonant inelastic x-ray scattering spectra, advancing quantum characterization techniques.

Contribution

It introduces a new entanglement witness based on four-fermion correlations derived from spectroscopic data, specifically addressing the challenge of indistinguishable electrons.

Findings

The method effectively extracts four-fermion correlations from spectra.

The entanglement witness scales linearly with entanglement depth.

It outperforms quantum Fisher information in quantifying multipartite entanglement.

Abstract

Characterizing entanglement in quantum materials is crucial for advancing next-generation quantum technologies. Despite recent strides in witnessing entanglement in magnetic materials with distinguishable spin modes, quantifying entanglement in systems formed by indistinguishable electrons remains a formidable challenge. To solve this problem, we introduce a method to extract various four-fermion correlations by analyzing the nonlinearity in resonant inelastic x-ray scattering spectra. These correlations constitute the primary components of the cumulant two-particle reduced density matrix. We further derive bounds for its eigenvalues and demonstrate the linear scaling with fermionic entanglement depth, providing a reliable witness for entanglement. Using the material-relevant strongly correlated models as examples, we show how this entanglement witness can efficiently quantify multipartite entanglement across different phase regions, highlighting its advantage over quantum Fisher information.