  We study the phase sensitivity in the conventional $SU(2)$ and
nonconventional $SU(1,1)$ interferometers with the coherent and squeezed vacuum
input state via the quantum Cramer-Rao bound. We explicitly construct the
detection scheme that gives the optimal phase sensitivity. For practical
purposes, we show that in the presence of photon loss, both interferometers
with proper homodyne detections, are nearly optimal. We also find that unlike
the coherent state and squeezed vacuum state, the effects of the imperfect
detector on the phase sensitivity cannot be asymptotically removed for a
generic coherent-squeezed state by increasing the amplifier gain of the OPA.
