Infinitesimal change is a Non-local Operation: Hidden power of Quantum Entanglement

Abstract

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.