  We study the influence of acceleration on the twin-Fock state which is a
class of specific multibody entangled quantum state and was already realized
experimentally with high precision and sensitivity. We show that the multi-body
quantum entanglement can be increased with the acceleration, consistent with
the "anti-Unruh effect" in reference to the counterintuitive cooling previously
pointed out for an accelerated detector coupled to the vacuum. In particular,
this kind of entanglement increase can lead to the improvement of the phase
sensitivity, which provides a way to test the anti-Unruh effect in the future
experiments.
