  We study the "anti-Unruh effect" for an entangled quantum state in reference
to the counterintuitive cooling previously pointed out for an accelerated
detector coupled to the vacuum. We show that quantum entanglement for an
initially entangled (spacelike separated) bipartite state can be increased when
either a detector attached to one particle is accelerated or both detectors
attached to the two particles are in simultaneous accelerations. However, if
the two particles (e.g., detectors for the bipartite system) are not initially
entangled, entanglement cannot be created by the anti-Unruh effect. Thus,
within certain parameter regime, this work shows that the anti-Unruh effect can
be viewed as an amplification mechanism for quantum entanglement.
