Spin correlation tensor for measurement of quantum entanglement in electron-electron scattering

TL;DR

This paper introduces a geometrical measure of quantum entanglement based on the spin correlation tensor in electron-electron scattering, demonstrating its validity and independence from certain rotations, with practical experimental implications.

Contribution

A novel geometrical entanglement measure using the spin correlation tensor for two-electron states, validated by theoretical properties and applicable to experiments.

Findings

The measure satisfies key properties of entanglement quantifiers.

It is independent of azimuthal rotation of the second electron's spin.

Practical method for experimental determination of entanglement in electron scattering.

Abstract

We consider the problem of correct measurement of a quantum entanglement in the two-body electron-electron scattering. An expression is derived for a spin correlation tensor of a pure two-electron state. A geometrical measure of a quantum entanglement as the distance between two forms of this tensor in entangled and separable cases is presented. We prove that this measure satisfies properties of a valid entanglement measure: nonnegativity, discriminance, normalization, non-growth under local operations and classical communication. This measure is calculated for a problem of electron-electron scattering. We prove that it does not depend on the azimuthal rotation angle of the second electron spin relative to the first electron spin before scattering. Finally, we specify how to find a spin correlation tensor and the related measure of a quantum entanglement in an experiment with electron-electron scattering.