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Departing from the usual paradigm of local operations and classicalcommunication adopted in entanglement theory, here we study the interconversionof quantum states by means of local operations and shared randomness. A set ofnecessary and sufficient conditions for the existence of such a transformationbetween two given quantum states is given in terms of the payoff they yield ina suitable class of nonlocal games. It is shown that, as a consequence of ourresult, such a class of nonlocal games is able to witness quantum entanglement,however weak, and reveal nonlocality in any entangled quantum state. An exampleillustrating this fact is provided.

All Entangled Quantum States Are Nonlocal