  We show that the global infinitesimal change in the multi-particle pure
product state gives rise to an entangled state. This suggests that even if
there is no interaction present between the subsystems, i.e., at each time
instant the state is non-entangled, the tangent vector is typically entangled.
Since the tangent space vectors tell the state-space vectors how to change this
implies that quantum entanglement is necessary for motion or change in general.
This is truly a `hidden power' of quantum entanglement. During quantum
computation even though at each time instant the state is not entangled,
quantum entanglement guides the process of computation. This observation
applies to multi-particle pure, pseudo-pure and mixed states as well.
