A nonlinear optical interferometric setup which is composed of three parts. Part I is for preparing the input states to the main body of the interferometer (Part II), and Part III is for detection. The prepared states from Part I and the pump light go through an OPA. There is a phase shifter in one arm of the interferometer, and the light will carry phase information after passing through it. Before the detection, there is a black box BB, which may be a BS or an OPA, which represents an MMZI or an SU(1,1)I, respectively. The homodyne detection is implemented to the output mode a₂.