  In extreme astrophysical environments such as core-collapse supernovae and
binary neutron star mergers, neutrinos play a major role in driving various
dynamical and microphysical phenomena, such as baryonic matter outflows, the
synthesis of heavy elements, and the supernova explosion mechanism itself. The
interactions of neutrinos with matter in these environments are
flavor-specific, which makes it of paramount importance to understand the
flavor evolution of neutrinos. Flavor evolution in these environments can be a
highly nontrivial problem thanks to a multitude of collective effects in flavor
space, arising due to neutrino-neutrino ($\nu$-$\nu$) interactions in regions
with high neutrino densities. A neutrino ensemble undergoing flavor
oscillations under the influence of significant $\nu$-$\nu$ interactions is
somewhat analogous to a system of coupled spins with long-range interactions
among themselves and with an external field ('long-range' in momentum-space in
the case of neutrinos). As a result, it becomes pertinent to consider whether
these interactions can give rise to significant quantum correlations among the
interacting neutrinos, and whether these correlations have any consequences for
the flavor evolution of the ensemble. In particular, one may seek to utilize
concepts and tools from quantum information science and quantum computing to
deepen our understanding of these phenomena. In this article, we attempt to
summarize recent work in this field. Furthermore, we also present some new
results in a three-flavor setting, considering complex initial states.
