The schemes are presented for realizing optical Bell-state and GHZ-state analyzers through the Faraday rotation, which results from polarization photon reflected by optical cavity with trapped atom. They can be extended to the case of completely distinguishing photon Bell-state and GHZ-state without destroying quantum qubit. In the schemes, strong-coupling condition is not needed and the analyzers can be implemented in low-Q cavity, which further lower the diffculty in experiment.