  We study the transport of few-photon states in an open disordered nonlinear
photonic lattice. More specifically, we consider a waveguide quantum
electrodynamics (QED) setup where photons are scattered from a chain of
nonlinear resonators with onsite Bose-Hubbard interaction in the presence of an
incommensurate potential. Applying our recently developed diagrammatic
technique that represents scattering matrix (S-matrix) with scattering diagrams
and associated propagators, we compute the two-photon transmission probability
and show that it carries signatures of the underlying many-body localization
transition of the system. We compare the calculated probability to the
participation ratio of the eigenstates and find close agreement for a range of
interaction strengths. We analyze the robustness of the transmission signatures
against local dissipation and briefly discuss possible implementation using
current superconducting circuit technology.
