  We compare three different characterizations of the globalness of bipartite
unitary operations, namely, delocalization power, entanglement cost, and
entangling power, to investigate global properties of unitary operations. We
show that the globalness of the same unitary operation depends on whether input
states are given by unknown states representing pieces of quantum information,
or a set of known states for the characterization. We extend our analysis on
the delocalization power in two ways. First, we show that the delocalization
power differs whether the global operation is applied on one piece or two
pieces of quantum information. Second, by introducing a new task called LOCC
one-piece relocation, we prove that the controlled-unitary operations do not
have the delocalization power strong enough to relocate one of two pieces of
quantum information by adding LOCC.
