Quantum entanglement in helium

Abstract

We compute the entanglement of the ground state and several singlet and triplet excited states of the helium atom using high-quality, state-of-the-art wavefunctions. The behaviour of the entanglement of the helium eigenstates is similar to that observed in some exactly soluble two-electron systems. In particular, the amount of entanglement exhibited by the eigenstates tends to increase with energy.

Doubly Excited Resonance States of Helium Atom: Complex Entropies

“…In particular, there has been a remarkable increase of interest in exploring properties of various quantum composite systems [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. In recent years, both the entanglement and Shannon Entropy in helium and helium-like ions have also accelerated a great research attention [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. However, studies on the correlation in resonance states have not yet drawn much attention.…”

The von Neumann entanglement entropy for Wigner-crystal states in one dimensional N-particle systems

“…For example, some light has been shed on entanglement both in quantum dot systems [6][7][8][9][10][11][12][13][14][15] and in systems of harmonically interacting particles in a harmonic trap (the so-called Moshinsky atom) [16][17][18][19][20][21][22][23]. Special attention has also been paid to the study of entanglement in the helium atoms and helium ions [24][25][26][27][28][29][30][31][32]. The effect of the confinement on the entanglement in the ground state of the helium atom has also been discussed in the literature [33].…”

Entanglement Computation in Atoms and Molecules

“…A computation of entanglement for a realistic model of the Helium atom can be found in [26]. The entanglement is evaluated computing the linear entropy, that implies to evaluate the trace of the squared reduced density matrix.…”

“…As the functions used as a basis in this work are expressed in terms of spatial coordinates, no simplifications are possible and it is necessary to evaluate a 12-dimensional integral, that was computed using Monte Carlo multidimensional numerical integration. The authors computed the linear entropy for several levels of the singlet and triplet; actually, the present work can be considered an extension of [26], as some more levels have been computed, and also the von Neumann entropy has been evaluated, because the method proposed herein computes the eigenvalues of the reduced density matrix.…”