  In [arXiv:2207.03377] the first closed formula of a faithful entanglement
measure applicable to realistic electron systems has been derived. In the
present work, we build on this key achievement with the ultimate goal of
guiding the development of quantum technologies. For this, we first elucidate
the process of entanglement swapping in electron systems such as atoms,
molecules or solid bodies. This clearly demonstrates the necessity of both the
reference to localized few-orbital subsystems and the implementation of the
number-parity superselection rule. Accordingly, in virtue of Wick's theorem, we
then provide a fully analytical study of the true physical entanglement between
sites in free electron chains. In that sense, we break the common paradigm of
restricting such analytical analyses to unitarily invariant settings, i.e.
bipartitions of the chain into rather impractical, macroscopically large
subsystems. We then upgrade this model to a hydrogen ring of interacting
electrons and construct the sought-after localized orbitals. For both systems,
we confirm the presence of long-distance entanglement, provided the filling
fractions are sufficiently low/high.
