All Entangled Quantum States Are Nonlocal

Departing from the usual paradigm of local operations and classical communication adopted in entanglement theory, we study here the interconversion of quantum states by means of local operations and shared randomness. A set of necessary and sufficient conditions for the existence of such a transformation between two given quantum states is given in terms of the payoff they yield in a suitable class of nonlocal games. It is shown that, as a consequence of our result, such a class of nonlocal games is able to witness quantum entanglement, however weak, and reveal nonlocality in any entangled quantum state. An example illustrating this fact is provided.

Figure 1

In a semiquantum nonlocal game (Def. 4), while players still reply with classical answers, the referee is allowed to ask quantum questions. Whenever the signals ${\tau }^s$ and ${\omega }^t$ are perfectly distinguishable, i.e., classical, the case of conventional nonlocal games (Def. 1) is recovered. By means of semiquantum nonlocal games, it is possible to show that all entangled quantum states are nonlocal (Cor. 1).