Entanglement concentration for concatenated Greenberger-Horne-Zeilinger state

The concatenated Greenberger-Horne-Zeilinger state is a new type of logic-qubit entanglement, which attracts a lot of attentions recently. In this paper, we discuss the entanglement concentration for such logic-qubit entanglement. We present two groups of entanglement concentration protocols (ECPs) for logic-qubit entanglement. In the first group, the parties do not know the initial coefficients of the partially logic-qubit entanglement. In the second group, the parties know the initial coefficients of the partially logic-qubit entanglement. In our ECPs, the unsuccessful cases can be reused to increase the total success probability in the next step. These ECPs may be useful in future long-distant quantum communication.