  We study quantum and classical Hanbury Brown-Twiss correlations in waveguide
lattices. We develop a theory for the propagation of photon pairs in the
lattice, predicting the emergence of nontrivial quantum interferences unique to
lattice systems. Experimentally, we observe the classical counterpart of these
interferences using intensity correlation measurements. We discuss the
correspondence between the classical and quantum correlations, and consider
path-entangled input states which do not have a classical analogue. Our results
demonstrate that waveguide lattices can be used as a robust and highly
controllable tool for manipulating quantum states, and offer new ways of
studying the quantum properties of light.
