  We propose a theoretical scheme to enhance the phase sensitivity by
introducing a Kerr nonlinear phase shift into the traditional SU(1,1)
interferometer with a coherent state input and homodyne detection. We
investigate the realistic effects of photon losses on phase sensitivity and
quantum Fisher information. The results show that compared with the linear
phase shift in SU(1,1) interferometer, the Kerr nonlinear case can not only
enhance the phase sensitivity and quantum Fisher information, but also
significantly suppress the photon losses. We also observe that at the same
accessible parameters, internal losses have a greater influence on the phase
sensitivity than the external ones. It is interesting that, our scheme shows an
obvious advantage of low-cost input resources to obtain higher phase
sensitivity and larger quantum Fisher information due to the introduction of
nonlinear phase element.
