Higher precision to estimate a phase via an optical interferometer with multiple passes

In this paper, we design a super-stable optical interferometer with multi-pass to estimate an unknown phase by using single photon, two-entangled photons, four-entangled photons and distinguishable four-photons. By jointing photon counting measurements, we find that these schemes enable us to estimate an unknown phase with a considerable high precision and beat the standard quantum limit under a certain condition.