Bell-state Analysis for Logic Qubits Entanglement

Decoherence is one of the main obstacles in long-distance quantum communication. Recently, the theoretical work of Fr\"{o}wis and W. D\"{u}r (Phys. Rev. Lett. \textbf{106}, 110402 (2011)) and the experiment of Lu \emph{et al.} (Nat. Photon. \textbf{8}, 364 (2014)) both showed that the logic qubits entanglement say the concatenated Greenberger-Horne-Zeilinger (C-GHZ) state is more robust under decoherence. In this paper, we describe a protocol for Bell-state analysis for this logic qubits entanglement. This protocol can also be extended to the multipartite C-GHZ state analysis. Also, we discuss its application in the quantum teleportation of a unknown logic qubit and in the entanglement swapping of logic Bell states. As the logic qubits entanglement is more robust under decoherence, our protocol shows that it is possible to realize the long-distance quantum communication based on logic qubits entanglement.