All entangled pure states violate a single Bell's inequality

TL;DR

This paper proves that all entangled pure states of multi-level particles violate a specific Bell's inequality, establishing the equivalence of Bell nonlocality and quantum entanglement for pure states.

Contribution

It generalizes Gisin's theorem to all entangled pure states with particles of varying energy levels using a single Bell's inequality.

Findings

All entangled pure states violate the inequality.

Bell nonlocality and entanglement are equivalent for pure states.

The result applies to particles with different energy levels.

Abstract

We show that a single Bell's inequality with two dichotomic observables for each observer, which is originated 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.