Bell's inequalities detect efficient entanglement

Abstract

We review the status of Bell's inequalities in quantum information, stressing mainly the links with quantum key distribution and distillation of entanglement. We also prove that for all the eavesdropping attacks using one qubit, and for a family of attacks of two qubits, acting on half of a maximally entangled state of two qubits, the violation of a Bell inequality implies the possibility of an efficient secret-key extraction.