  We study how two pieces of localized quantum information can be delocalized
across a composite Hilbert space when a global unitary operation is applied. We
classify the delocalization power of global unitary operations on quantum
information by investigating the possibility of relocalizing one piece of the
quantum information without using any global quantum resource. We show that
one-piece relocalization is possible if and only if the global unitary
operation is local unitary equivalent of a controlled-unitary operation. The
delocalization power turns out to reveal different aspect of the non-local
properties of global unitary operations characterized by their entangling
power.
