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The concatenated Greenberger-Horne-Zeilinger (C-GHZ) state has greatpotential application in the future quantum network, for it is robust to thedecoherence in a noisy environment. In the paper, we propose a complete C-GHZstate analysis protocol with the help of some auxiliary single atoms trapped inthe low-quality cavities. In the protocol, we essentially make the parity checkfor the photonic states based on the photonic Faraday rotation effect, andcomplete the analysis task combined with the Hadamard operation and singlequbit measurement. The success probability of our protocol can reach 100\% inprinciple, and the number of physical qubit encoded in each logic qubit doesnot affect the analysis. Our analysis protocol may have its practicalapplication in future long-distance quantum communication.

Complete analysis for arbitrary concatenated Greenberger-Horne-Zeilinger state assisted with photonic Faraday rotation