Several schemes are proposed to realize the conversion of photonic polarized-entangled Greenberger-Horne-Zeilinger state to Knill-Laflamme-Milburn state in decoherence-free subspace (DFS) via weak cross-Kerr nonlinearity and X-quadrature homodyne measurement with high fidelity. DFS is introduced to decrease the decoherence effect caused by the coupling between the system and the environment. Optimizations to improve the success rate and utilization of residual states are further investigated. This study indicates important applications for quantum information processing in the future.
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