Features of Non-Local Quantum Correlations in Nuclei
Classical simulation of quantum many-body systems is challenged by the combined effects of entanglement and non-stabilizerness (magic). Non-local magic, $M^{\mathrm{NL}}_α$, quantifies the component of non-stabilizerness that cannot be removed by local unitary transformations and provides a measure of quantum complexity beyond entanglement alone. It is bounded from below by the antiflatness of the entanglement spectrum, ${F}_A$. We calculate stabilizer Rényi entropies, non-local magic, entanglement-spectrum antiflatness, and entanglement entropy in shell-model ground states of more than 260 even-even, odd-even, and odd-odd nuclei, using a bipartition into proton and neutron sectors. We find that the previously established bound $4{F}_A\leq{M}^{\mathrm{NL}}_{\mathrm{lin}}$ holds for every nucleus studied and approaches saturation in the limit of separable states. Odd-odd nuclei exhibit markedly different patterns of entanglement and magic compared with even-even and odd-even systems, revealing distinctive signatures of proton-neutron quantum correlations and providing new insight into the complexity generated by nuclear interactions.