Feasible quantum engineering of quantum multiphoton superpositions

We examine an experimental setup implementing a family of quantum non-Gaussian filters. The filters can be applied to an arbitrary two-mode input state. We assume realistic photodetection in the filtering process and explore two different models of inefficient detections: a beam splitter of a small reflectivity located in front of a perfect detector and a Weierstrass transform applied to the unperturbed measurement outcomes. We explicitly give an operator which describes the coherent action of the filters in the realistic experimental conditions. The filtered states may find applications in quantum metrology, quantum communication and other quantum tasks.