Quantum Entanglement and Shannon Information Entropy for the Doubly Excited Resonance State in Positronium Negative Ion

Chien-Hao Lin,Yew Ho

doi:10.3390/atoms3030422

Chien-Hao Lin, Yew Ho

Open Access

https://doi.org/10.3390/atoms3030422

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Abstract

In the present work, we report an investigation on quantum entanglement in the doubly excited 2s2 1Se resonance state of the positronium negative ion by using highly correlated Hylleraas type wave functions, determined by calculation of the density of resonance states with the stabilization method. Once the resonance wave function is obtained, the spatial (electron-electron orbital) entanglement entropies (von Neumann and linear) can be quantified using the Schmidt decomposition method. Furthermore, Shannon entropy in position space, a measure for localization (or delocalization) for such a doubly excited state, is also calculated.

Highlights

Considerable research activities have been carried out on investigations of quantum entanglement in model, artificial, and natural atoms [1,2,3,4,5,6,7,8]
We report quantification of entropies for the doubly excited 2s2 1 S e state in the positronium negative ion
The results of the three plateaus for the resonance states are listed in Table 1, and it shows that plateau “I” gives the best fit as its r2 is closest to the ideal value of 1.0

Summary

Introduction

Considerable research activities have been carried out on investigations of quantum entanglement in model, artificial, and natural atoms [1,2,3,4,5,6,7,8]. Our recent works include studies on spatial (electron-electron orbital) entanglement in highly correlated two-electron systems such as the helium atom, the hydrogen and positronium negative ions [12,13,14,15,16]. By using highly-corrected Hylleraas-type wave functions to represent the ground and singly-excited states of such systems, we have established benchmark values for von Neumann and linear entropies in the two-electron atom/ions [14,15,16]. We report quantification of entropies (von Neumann, linear, and Shannon information) for the doubly excited 2s2 1 S e state in the positronium negative ion. The resonance wave function is used to calculate the Shannon information entropy in positon space to probe the classical correlation of the doubly excited state in positronium negative ion.

The Stabilization Method

Von Neumann and Linear Entropies

Shannon Information Entropy

Results and Discussion

Section III

Conclusions