We show that a single Bell’s inequality with two dichotomic observables for each observer, which originates from Hardy’s nonlocality proof without inequalities, is violated by all entangled pure states of a given number of particles, each of which may have a different number of energy levels. Thus Gisin’s theorem is proved in its most general form from which it follows that for pure states Bell’s nonlocality and quantum entanglement are equivalent.

• Received 7 May 2012

DOI:https://doi.org/10.1103/PhysRevLett.109.120402