  One of the active debates in core-collapse supernova (CCSN) theory is how
significantly neutrino flavor conversions induced by neutrino-neutrino
self-interactions change the conventional picture of CCSN dynamics. Recent
studies have indicated that strong flavor conversions can occur inside neutrino
spheres where neutrinos are tightly coupled to matter. These flavor conversions
are associated with either collisional instability or fast neutrino-flavor
conversion (FFC) or both. The impact of these flavor conversions on CCSN
dynamics is, however, still highly uncertain due to the lack of global
simulations of quantum kinetic neutrino transport with appropriate
microphysical inputs. Given fluid profiles from a recent CCSN model at three
different time snapshots in the early post-bounce phase, we perform global
quantum kinetic simulations in spherical symmetry with an essential set of
microphysics. We find that strong flavor conversions occur in optically thick
regions, resulting in a substantial change of neutrino radiation field. The
neutrino heating in the gain region is smaller than the case with no flavor
conversions, whereas the neutrino cooling in the optically thick region is
commonly enhanced. Based on the neutrino data obtained from our multi-angle
neutrino transport simulations, we also assess some representative classical
closure relations by applying them to diagonal components of density matrix of
neutrinos. We find that Eddington tensors can be well approximated by these
closure relations except for the region where flavor conversions occur vividly.
We also analyze the neutrino signal by carrying out detector simulations for
Super-Kamiokande, DUNE, and JUNO. We propose a useful strategy to identify the
sign of flavor conversions in neutrino signal, that can be easily implemented
in real data analyses of CCSN neutrinos.
