  Realizing an on-chip reconfigurable source of path-entangled photons is of
critical importance for the advancement of quantum information processing and
networking. Achieving this goal has proven challenging to date. We present an
on-chip scheme for the deterministic creation of co-propagating or
counter-propagating path-entangled photon pairs that can be routed in multiple
configurations by tuning a classical parameter. The simplest manifestation of
this approach makes use of two \textit{coupled} waveguides: a
\textit{nonlinear} waveguide that produces photon pairs via spontaneous
parametric downconversion from an externally incident unguided optical pump,
and an auxiliary \textit{linear} waveguide. Although the photon pairs are born
in only one waveguide, which alone cannot create path-entanglement, linear
coupling over an extended length to the passive waveguide introduces unexpected
indistinguishability that induces path-entanglement. Tuning of the classical
pump spatial profile allows routing the photon pairs over all possible
configurations. The proposed device is a building block for future
quantum-optical networks.
