  We investigate the resonance quadrupole-quadrupole interaction between two
entangled gravitationally polarizable objects induced by a bath of fluctuating
quantum gravitational fields in vacuum in the framework of linearized quantum
gravity. Our result shows that, the interaction energy behaves as $r^{-5}$ in
the near regime, and oscillates with a decreasing amplitude proportional to
$r^{-1}$ in the far regime, where $r$ is the distance between the two objects.
Compared to the case when the two objects are in their ground states, the
quantum gravitational interaction is significantly enhanced when the objects
are in an entangled state. Remarkably, in the far regime, the resonance quantum
gravitational interaction can give the dominating quantum correction to the
Newtonian potential, since the extremum is much greater than the
monopole-monopole quantum gravitational interaction.
