Simultaneously estimating two phase shifts with a power-recycled tri-port interferometer fed by coherent states

Supersensitive phase estimation was and is one of the principal goals in the field of precision measurements. In this paper, we study a power-recycled tri-port interferometer that enables the protocol to estimate two phase shifts simultaneously. Each sensitivity of the phase shift is the shot-noise limit 1/N with two coherent states as inputs (3N/2 photons on average), and the balanced homodyne detection is performed on the outputs. Fundamental sensitivity limits of two estimated phases are studied by calculating the quantum Fisher information. Finally, we discuss the effects of photon loss on the phase sensitivity.