  By means of the Dirac bispinor formalism, we show that the state of a
(massive) oscillating neutrino produced by a weak interaction process, is an
hyperentangled state of flavor, chirality, and spin. Since chirality is not a
conserved quantity, chiral oscillations take place and affects the flavor
transition probability. By means of the complete complementarity relations, we
analyze how correlations and coherence are redistributed in time between the
different degrees-of-freedoms of the system. In a similar way, we consider a
spin entangled lepton-antineutrino pair and describe the redistribution of the
spin-spin entanglement into correlations between the other degrees-of-freedom.
In both cases the effects of chiral oscillations are relevant in the
non-relativistic regime. Our analysis provides a complete characterization of
the quantum correlations involved in lepton-antineutrino pairs and in single
particle neutrino evolution, and provides a further insight on possible routes
to interpret and measure chiral oscillations.
