Mermin inequalities for perfect correlations

Abstract

Any n-qubit state with n independent perfect correlations is equivalent to a graph state. We present the optimal Bell inequalities for perfect correlations and maximal violation for all classes of graph states with n < 7 qubits. Twelve of them were previously unknown and four give the same violation as the Greenberger-Horne-Zeilinger state, although the corresponding states are more resistant to decoherence.