Comparing the globalness of bipartite unitary operations: delocalisation power, entanglement cost and entangling power

摘要

We compare three different characterisations of the globalness of bipartite unitary operations, namely, delocalisation power, entanglement cost and entangling power, to investigate the 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 characterisation. We extend our analysis of delocalisation power in two ways. First we show that the delocalisation power differs according to whether the global operation is applied to one piece or two pieces of quantum information. Then we introduce a new task called LOCC one-piece relocation, and prove that the controlled-unitary operations do not have enough delocalisation power to relocate one of two pieces of quantum information by adding LOCC.