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Abstract

In general, there is a class of information processing tasks that cannot be accomplished when operations are restricted to local operations and classical communication(LOCC). When global tasks are to be accomplished, certain properties of nonlocal (i.e., global) unitary operations are needed, where these properties are collectively referred to as globalness, in this work. It can be argued that the globalness of unitary operations is an important resource for realizing extra-classical performances in quantum information processing. In this work, we focus on globalness of unitary operations that are particularly relevant to global tasks dealing with unknown input states, and analyze this globalness by studying three global tasks, which we call (i) two-piece delocalization, (ii) one-piece delocalization, and (iii) entanglement-assisted LOCC implementation of global unitary operations. Based on these analyses of the three global tasks (i)-(iii), we argue that they naturally lead to characterizations of globalness. Moreover, these characterizations, which are all based on global tasks on unknown input states, are compared against a characterization based on a global task on known input states, called entangling power. We find that entangling power is unrelated to the characterizations based on the global tasks on unknown input states. It is argued that the degree of globalness of unitary operations reflects the fundamental difference between the known and unknown input states in the task used to characterize the globalness.