  Bell states are a fundamental resource in photonic quantum information
processing. These states have been generated successfully in many photonic
degrees of freedom. Their manipulation, however, in the momentum space remains
challenging. Here, we present a scheme for engineering the symmetry of
two-photon states entangled in the transverse momentum degree of freedom
through the use of a spatially variable phase object. We demonstrate how a
Hong-Ou-Mandel interferometer must be constructed to verify the symmetry in
momentum entanglement via photon "bunching"/"anti-bunching" observation. We
also show how this approach allows generating states that acquire an arbitrary
phase under the exchange operation.
