Quantum entanglement provides a unique perspective for probing nuclear structure. In this work, we employ quantum entanglement measures, including proton-neutron entanglement entropy, mutual information, and quantum relative entropy, to investigate the evolution of entanglement patterns as we approach neutron-rich nuclei. The study is carried out in the vicinity of the $N=20$ island of inversion region consisting of even-$A$ Ne, Mg, and Si isotopes, and also for isotones corresponding to $N=20$. The state-of-the-art ab initio valence space in-medium similarity renormalization group method is used for this purpose. We highlight the role of proton-neutron entanglement entropy in the formation of the island of inversion region. Mutual information provides insight into the strength of correlations between proton-proton, neutron-neutron, and proton-neutron single-particle states. While these correlations are relatively weak between protons and neutrons in the ground states, they become comparable to like-particle correlations in excited states. The quantum relative entropy is also studied between $0^{+}$ and $2^{+}$ states of the Ne, Mg, and Si isotopes, as well as $N=20$ isotones, using the Kullback-Leibler divergence and Jensen-Shannon divergence. We perform these calculations by expressing the nuclear wave functions in a Slater-determinant basis and analyzing them through complementary partitions, including proton-neutron and mode-resolved factorizations.

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• Nuclear structure & decays
• Quantum correlations in quantum information
• Ab initio calculations