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. 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. This
analysis provides a guide for designing more efficient quantum algorithms for
the noisy intermediate-scale quantum era.Comment: Submitted to EPJA Topical Issue "Quantum computing in low-energy
nuclear theory