Fig. 1: Generic QPIC with two input and output channels.

It is assumed that pairs of polaritons are created at x = 0 and many-body interactions are then detected at xD by measuring the degree of correlation of photons emerging from the two channels. In this work, we will assume that each input is a single photon state. The device consists of a sequence of N interaction regions of length lj (j = 1, 2, ⋯ N) where the two waveguides (labeled as A and B) run in parallel at a distance equal to d so that they are evanescently coupled. Two consecutive interaction regions are separated by a free-propagation region, that is a portion of the device where the distance between the two waveguides is D ≫ d and the coupling between the two waveguides is negligible.