Quantum entanglement patterns in the structure of atomic nuclei within the nuclear shell model

TL;DR

This paper applies quantum information tools to analyze entanglement patterns in atomic nuclei within the nuclear shell model, revealing correlations related to energy, pairing, and deformation, and guiding quantum algorithm design.

Contribution

It introduces a comprehensive quantum entanglement analysis of nuclear structure, linking entanglement metrics to nuclear properties and informing quantum computational approaches.

Findings

Single-orbital entanglement correlates with valence nucleon number and shell energy.

Mutual information reveals proton-proton and neutron-neutron pairing signatures.

Proton and neutron orbitals are weakly entangled compared to others.

Abstract

Quantum entanglement offers a unique perspective into the underlying structure of strongly-correlated systems such as atomic nuclei. In this paper, we use quantum information tools to analyze the structure of light and medium-mass berillyum, oxygen, neon and calcium isotopes within the nuclear shell model. We use different entanglement metrics, including single-orbital entanglement, mutual information, and von Neumann entropies for different equipartitions of the shell-model valence space and identify mode-entanglement patterns related to the energy, angular momentum and isospin of the nuclear single-particle orbitals. We observe that the single-orbital entanglement is directly related to the number of valence nucleons and the energy structure of the shell, while the mutual information highlights signatures of proton-proton and neutron-neutron pairing, as well as nuclear deformation. Proton and neutron orbitals are weakly entangled by all measures, and in fact have the lowest von Neumann entropies among all possible equipartitions of the valence space. In contrast, orbitals with opposite angular momentum projection have relatively large entropies, especially in spherical nuclei. This analysis provides a guide for designing more efficient quantum algorithms for the noisy intermediate-scale quantum era.