  To improve the phase sensitivity, multi-photon subtraction schemes within the
SU(1,1) interferometer are proposed. The input states are the coherent state
and the vacuum state, and the detection method is homodyne detection. The
effects of multi-photon subtraction on phase sensitivity, quantum Fisher
information, and quantum Cramer-Rao bound are analyzed under both ideal and
photon losses situations. It is shown that the internal subtraction operation
can improve the phase sensitivity, which becomes better performance by
increasing subtraction number. It can also efficiently improve the robustness
of the SU(1,1) interferometer against internal photon losses. By comparing
separatively arbitrary photon subtraction on the two-mode inside SU(1,1)
interferometer, the performance differences under different conditions are
analyzed, including the asymmetric properties of non-Gaussian operations on the
phase precision and the quantum Fisher information. Our proposed scheme
represents a valuable method for achieving quantum precision measurements.
