  Fourth-order interference is an information processing primitive for photonic
quantum technologies. When used in conjunction with post-selection, it forms
the basis of photonic controlled logic gates, entangling measurements, and can
be used to produce quantum correlations. Here, using classical weak coherent
states as inputs, we study fourth-order interference in novel $4 \times 4$
multi-port beam splitters built within multi-core optical fibers. Using two
mutually incoherent weak laser pulses as inputs, we observe high-quality fourth
order interference between photons from different cores, as well as
self-interference of a two-photon wavepacket. In addition, we show that quantum
correlations, in the form of quantum discord, can be maximized by controlling
the intensity ratio between the two input weak coherent states. This should
allow for the exploitation of quantum correlations in future telecommunication
networks.
