Nonlocal content of quantum operations

We show that quantum operations on multiparticle systems have a nonlocal content; this mirrors the nonlocal content of quantum states. We introduce a general framework for discussing the nonlocal content of quantum operations, and give a number of examples. Quantitative relations between quantum actions and the entanglement and classical communication resources needed to implement these actions are also described. We also show how entanglement can catalyze classical communication from a quantum action.