We initiate the study of quantifying nonlocalness of a bipartite measurementby the minimum amount of classical communication required to simulate themeasurement. We derive general upper bounds, which are expressed in terms ofcertain tensor norms of the measurement operator. As applications, we show that(a) If the amount of communication is constant, quantum and classicalcommunication protocols with unlimited amount of shared entanglement or sharedrandomness compute the same set of functions; (b) A local hidden variable modelneeds only a constant amount of communication to create, within an arbitrarilysmall statistical distance, a distribution resulted from local measurements ofan entangled quantum state, as long as the number of measurement outcomes isconstant.
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