  We calculate coherent neutrino and antineutrino flavor transformation in the
supernova environment, for the first time including a self-consistent treatment
of forward scattering-induced coupling and entanglement of intersecting
neutrino/antineutrino trajectories. For the atmospheric neutrino mass-squared
difference we find that in the normal (inverted) mass hierarchy the more
tangentially-propagating (radially-propagating) neutrinos and antineutrinos can
initiate collective, simultaneous medium-enhanced flavor conversion of these
particles across broad ranges of energy and propagation direction. Accompanying
alterations in neutrino/antineutrino energy spectra and/or fluxes could affect
supernova nucleosynthesis and the expected neutrino signal.
