  Simulation tasks are insightful tools to compare information-theoretic
resources. Considering a generalization of usual Bell scenarios where external
quantum inputs are provided to the parties, we show that any entangled quantum
state exhibits correlations that cannot be simulated using only shared
randomness and classical communication, even when the amount and rounds of
classical communication involved are unrestricted. We indeed construct explicit
Bell-like inequalities that are necessarily satisfied by such classical
resources but nevertheless violated by correlations obtainable from entangled
quantum states, when measured a single copy at a time.
