  Gravity induced neutrino-antineutrino oscillations are studied in the context
of one and two flavor scenarios. This allows one to investigate the
particle-antiparticle correlations in two and four level systems, respectively.
Flavor entropy is used to probe the entanglement in the system. The well known
witnesses of non-classicality such as Mermin and Svetlichly inequalities are
investigated. Since the extent of neutrino-antineutrino oscillation is governed
by the strength of the gravitational field, the behavior of non-classicality
shows interesting features as one varies the strength of the gravitational
field. Specifically, the suppression of the entanglement with the increase of
the gravitational field is observed which is witnessed in the form of decrease
in the flavor entropy of the system. The features of the Mermin and the
Svetlichny inequalities allow one to make statements about the degeneracy of
neutrino mass eigenstates.
