Phase sensitivity of an SU(1,1) interferometer in photon-loss via photon operations

We study the phase sensitivity of an SU(1,1) interferometer with photon loss by using three different photon operations schemes, i.e., performing photon-addition operation on the input port of the SU(1,1) interferometer (Scheme A), the interior of SU(1,1) interferometer (Scheme B), and both of them (Scheme C). We compare the performance of the three schemes in phase estimation by performing the same times of photon-addition operation to the mode b. The results show that Scheme B improves the phase sensitivity best in ideal case, and Scheme C performs well against internal loss, especially in the case of strong loss. All the three schemes can beat the standard quantum limit in the presence of photon loss, but Scheme B and Scheme C can break through the standard quantum limit in a larger loss range.