  Interference between independently generated photons is a key step towards
distributing entanglement over long distances, but it requires synchronization
between the distantly-located photon sources. Synchronizing the clocks of such
photon sources using coexisting two-way classical optical communications over
the same fiber that transport the quantum photonic signals is a promising
approach for achieving photon-photon interference over long distances, enabling
entanglement distribution for quantum networking using the deployed fiber
infrastructure. Here, we demonstrate photon-photon interference by observing
the Hong-Ou-Mandel dip between two distantly-located sources: a weak coherent
state source obtained by attenuating the output of a laser and a heralded
single-photon source. We achieve a maximum dip visibility of $0.58 \pm 0.04$
when the two sources are connected via $4.3$ km of deployed fiber. Dip
visibilities $>0.5$ are nonclassical and a first step towards achieving
teleportation over the deployed fiber infrastructure. In our experiment, the
classical optical communication is achieved with $-21$ dBm of optical signal
launch power, which is used to synchronize the clocks in the two independent,
distantly-located photon sources. The impact of spontaneous Raman scattering
from the classical optical signals is mitigated by appropriate choice of the
quantum and classical channel wavelengths. All equipment used in our experiment
(the photon sources and the synchronization setup) is commercially available.
Finally, our experiment represents a scalable approach to enabling practical
quantum networking with commercial equipment and coexistence with classical
communications in optical fiber.
