We study the phase sensitivity in the conventional $SU(2)$ andnonconventional $SU(1,1)$ interferometers with the coherent and squeezed vacuuminput state via the quantum Cramer-Rao bound. We explicitly construct thedetection scheme that gives the optimal phase sensitivity. For practicalpurposes, we show that in the presence of photon loss, both interferometerswith proper homodyne detections, are nearly optimal. We also find that unlikethe coherent state and squeezed vacuum state, the effects of the imperfectdetector on the phase sensitivity cannot be asymptotically removed for ageneric coherent-squeezed state by increasing the amplifier gain of the OPA.
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