Quantification of linear entropy for quantum entanglement in He, H- and Ps- ions using highly-correlated Hylleraas functions

TL;DR

This paper calculates the linear entropy as a measure of quantum entanglement in three two-electron atomic systems using highly correlated Hylleraas functions, providing analytical solutions for complex integrals.

Contribution

It introduces an analytical method to compute four-electron integrals for entanglement measures in three-body atomic systems using Hylleraas functions.

Findings

Calculated linear entropy values for He, H-, and Ps- ions.

Compared results with existing calculations for validation.

Provided analytical solutions suitable for machine computation.

Abstract

The quantum entanglement for the two electrons in three-body atomic systems such as the helium atom, the hydrogen negative ion and the positronium negative ion are investigated by employing highly correlated Hylleraas functions to represent the ground states of such systems. As a measure of the spatial entanglement, the linear entropy of the reduced density matrix is calculated for the ground states. The required four-electron (12-dimensional) integrals are solved analytically such that they are suitable for machine computations. Results are compared with other calculations when available.