Delocalization power of global unitary operations on quantum information

We investigate how originally localized two pieces of quantum information represented by a tensor product of two unknown qudit states are delocalized by performing two-qudit global unitary operations. To characterize the delocalization power of global unitary operations on quantum information, we analyze the necessary and sufficient condition to deterministically relocalize one of the two pieces of quantum information to its original Hilbert space by using only LOCC. We prove that this LOCC one-piece relocalization is possible if and only if the global unitary operation is local unitary equivalent to a controlled-unitary operation. The delocalization power and the entangling power characterize different non-local properties of global unitary operations.