  Entanglement properties of $^4$He and $^6$He are investigated using nuclear
many-body calculations, specifically the single-nucleon entanglement entropy,
and the two-nucleon mutual information and negativity. Nuclear wavefunctions
are obtained by performing active-space no-core configuration-interaction
calculations using a two-body nucleon-nucleon interaction derived from chiral
effective field theory. Entanglement measures within single-particle bases, the
harmonic oscillator (HO), Hartree-Fock (HF), natural (NAT) and variational
natural (VNAT) bases, are found to exhibit different degrees of complexity.
Entanglement in both nuclei is found to be more localized within NAT and VNAT
bases than within a HO basis for the optimal HO parameters, and, as
anticipated, a core-valence (tensor product) structure emerges from the full
six-body calculation of $^{6}$He. The two-nucleon mutual information shows that
the VNAT basis, which typically exhibits good convergence properties,
effectively decouples the active and inactive spaces. We conclude that measures
of one- and two-nucleon entanglement are useful in analyzing the structure of
nuclear wave functions, in particular the efficacy of basis states, and may
provide useful metrics toward developing more efficient schemes for ab initio
computations of the structure and reactions of nuclei, and quantum many-body
systems more generally.
