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We theoretically present the quantum Cram\'{e}r-Rao bounds (QCRB) of anSU(1,1) interferometer for Gaussian states input with and without the internalphotonic losses. The phase shifts in the single arm and in the double arms arestudied and the corresponding analytical expressions of quantum Fisherinformation with Gaussian input states are presented. Different from thetraditional Mach-Zehnder interferometer, the QCRB of single arm case isslightly higher or lower than that of double arms case depending on the inputstates. With a fixed mean photon number and for pure Gaussian state input, theoptimal sensitivity is achieved with a squeezed vacuum input in one mode andthe vacuum input in the other. We compare the QCRB with the standard quantumlimit and Heisenberg limit. In the case of small internal losses the QCRB canbeat the standard quantum limit.

Phase estimation of phase shifts in two arms for an SU(1,1) interferometer with coherent and squeezed vacuum states