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We analytically prove the necessary and sufficient criterion for the fullseparability of three-qubit Greenberger-Horne-Zeilinger (GHZ) diagonal states.The corresponding entanglement is exactly calculable for some GHZ diagonalstates and is tractable for the others using the relative entropy ofentanglement. We show that the biseparable criterion and the genuineentanglement are determined only by the biggest GHZ diagonal element regardlessof all the other smaller diagonal elements. We have completely solved theentanglement problems of three-qubit GHZ diagonal states.

Entanglement and genuine entanglement of three qubit GHZ diagonal states