Violation of Bell's inequalities and distillability for N qubits

We consider quantum systems composed of N qubits, and the family of all Bell's correlation inequalities for two two-valued measurements per site. We show that if an N-qubit state ρ violates any of these inequalities, then it is at least bipartite distillable. Indeed there exists a link between the amount of Bell's inequality violation and the degree of distillability. Thus, we strengthen the interpretation of Bell's inequalities as detectors of useful entanglement.