  The concept of `flat optics' is quickly conquering different fields of
photonics, but its implementation in quantum optics is still at infancy. In
particular, polarization entanglement, which is central to quantum photonics
due to the simplicity of polarization qubit encoding and control, is so far not
realized on flat platforms. Meanwhile, relaxed phase matching of flat nonlinear
optical sources enables enormous freedom in tailoring their polarization
properties. Here we use this freedom to generate photon pairs with tunable
polarization entanglement via spontaneous parametric down-conversion (SPDC) in
a $400$ nm GaP film. By changing the pump polarization, we tune the
polarization state of photon pairs from maximally entangled to almost
disentangled, which is impossible in a single bulk source of SPDC. Polarization
entanglement, in combination with the broadband frequency spectrum, results in
an ultranarrow (12 fs) Hong-Ou-Mandel effect and promises extensions to
hyperentanglement.
