Bell-Klyshko inequalities to characterize maximally entangled states of n qubits.

This Letter presents the first rigorous proof of the conjecture raised by Gisin and Bechmann-Pasquinucci [Phys. Lett. A 246, 1 (1998)]], that the Greenberger-Horne-Zeilinger states of n qubits and the states obtained from them by local unitary transformations are the unique states that maximally violate the Bell-Klyshko inequalities. The proof is obtained by using the certain algebraic properties that Pauli's matrices satisfy and some subtle mathematical techniques. Since all states obtained by local unitary transformations of a maximally entangled state are equally valid entangled states, we thus give a characterization of maximally entangled states of n qubits in terms of the Bell-type inequality.