Necessary and sufficient condition for Greenberger-Horne-Zeilinger diagonal states to be full $N$-partite entangled

Abstract

Recently, [{arXiv:0810.3134}] is accepted and published. We show that any $N$-qubit state which is diagonal in the Greenberger-Horne-Zeilinger basis is full $N$-qubit entangled state if and only if no partial transpose of the multiqubit state is positive with respect to any partition.