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Quantum entanglement offers a unique perspective into the underlyingstructure of strongly-correlated systems such as atomic nuclei. In this paper,we use quantum information tools to analyze the structure of light andmedium-mass berillyum, oxygen, neon and calcium isotopes within the nuclearshell model. We use different entanglement metrics, including single-orbitalentanglement, mutual information, and von Neumann entropies for differentequipartitions of the shell-model valence space and identify mode-entanglementpatterns related to the energy, angular momentum and isospin of the nuclearsingle-particle orbitals. We observe that the single-orbital entanglement isdirectly related to the number of valence nucleons and the energy structure ofthe shell, while the mutual information highlights signatures of proton-protonand neutron-neutron pairing, as well as nuclear deformation. Proton and neutronorbitals are weakly entangled by all measures, and in fact have the lowest vonNeumann entropies among all possible equipartitions of the valence space. Incontrast, orbitals with opposite angular momentum projection have relativelylarge entropies, especially in spherical nuclei. This analysis provides a guidefor designing more efficient quantum algorithms for the noisyintermediate-scale quantum era.

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