Synthesis of arbitrary interference patterns with high visibility

In recent years there have been many demonstrations of phase super-resolution - previously thought to be a manifestly quantum phenomenon - using classical light, but at the expense of reduced interference visibility. It is therefore of interest to delineate what interference effects belong to the realm of classical world, and which require quantum states. Generalizing Hofmann´s method of post-selection projection, we show that essentially any interference curve can be synthesized with high visibility with coherent state input. The method is based on the mathematical observation that any polynomial can be completely factored over the field of complex numbers. Hence, any two-mode, N-photon state can be written as a product of N single-photon, two-mode states, and the corresponding measurement projector can be experimentally implemented using beam splitters, phase-shifters, and N-photon coincidence measurements.