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We theoretically study the quantum Fisher information (QFI) of the SU(1,1)interferometer with phase shifts in two arms taking account of realistic noiseeffects. A generalized phase transform including the phase diffusion effect ispresented by the purification process. Based on this transform, the analyticalQFI and the bound to the quantum precision are derived when considering theeffects of phase diffusion and photon losses simultaneously. To beat thestandard quantum limit with the reduced precision of phase estimation due tonoisy, the upper bounds of decoherence coefficients as a function of total meanphoton number are given.

Phase estimation for an SU(1,1) interferometer in the presence of phase diffusion and photon losses