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We theoretically study the effect of quantum statistics of the light field onthe quantum enhancement of parameter estimation based on cat state input theSU(1,1) interferometer. The phase sensitivity is dependent on the relativephase $\theta$ between two coherent states of Schr\"{o}dinger cat states. Theoptimal sensitivity is achieved when the relative phase is $\pi$% , i.e., oddcoherent states input. For a coherent state input into one port, the phasesensitivity of the odd coherent state into the second input port is inferior tothat of the squeezed vacuum state input. However, in the presence of losses theSchr\"{o}dinger cat states are more resistant to loss than squeezed vacuumstates. As the amplitude of Schr\"{o}dinger cat states increases, the quantumenhancement of phase sensitivity decreases, which shows that the quantumstatistics of Schr\"{o}dinger cat states tends towards Poisson statistics fromsub-Poisson statistics or super-Poisson statistics.

The effect of Quantum Statistics on the sensitivity in an SU(1,1) interferometer