  Classical interferometers are indispensable tools for the precise
determination of various physical quantities. Their accuracy is bound by the
standard quantum limit. This limit can be overcome by using quantum states or
nonlinear quantum elements. Here, we present the experimental study of a
nonlinear Josephson interferometer operating in the microwave regime. Our
quantum microwave parametric interferometer (QUMPI) is based on superconducting
flux-driven Josephson parametric amplifiers combined with linear microwave
elements. We perform a systematic analysis of the implemented QUMPI. We find
that its Gaussian interferometric power exceeds the shot-noise limit and
observe sub-Poissonian photon statistics in the output modes. Furthermore, we
identify a low-gain operation regime of the QUMPI which is essential for
optimal quantum measurements in quantum illumination protocols.
