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Concatenated Greenberger-Horne-Zeilinger (C-GHZ) state, which encodes many physical qubits in a logic qubit will have important applications in both quantum communication and computation. In this paper, we will describe an entanglement concentration protocol (ECP) for electronic C-GHZ state, by exploiting the electronic polarization beam splitters (PBSs) and charge detection. This protocol has several advantages. First, the parties do not need to know the exact coefficients of the initial less-entangled C-GHZ state, which makes this protocol feasible. Second, with the help of charge detection, the distilled maximally entangled C-GHZ state can be remained for future application. Third, this protocol can be repeated to obtain a higher success probability. We hope that this protocol can be useful in future quantum computation based on electrons.

We describe an entanglement concentration protocol (ECP) for arbitrary four-photon less-entangled cluster state. The ECP works with the help of quantum nondemolition (QND) measurement and conventional photon detectors. In our ECP, an arbitrary less-entangled four-photon cluster state can be concentrated in two steps. Moreover, in both concentration steps, the discarded states can be reused to obtain a higher success probability. This protocol may be useful in current one-way quantum computation.

In this paper, we put forward an effective ECP for arbitrary less-entangled N-atom GHZ state with the help of the photonic Faraday rotation. In our protocol, we only require one pair of less-entangled atom state, one auxiliary atom and one auxiliary photon, and can complete the concentration task with relatively high success probability. Moreover, our ECP can be used repeatedly to further increase the success probability. Especially, if consider the practical operation and imperfect detection, our protocol is more efficient. This ECP may be useful in current quantum information processing.