  We analyze theoretically spontaneous parametric down-conversion in a
multimode nonlinear waveguide as a source of entangled pairs of spatial qubits,
realized as superpositions of a photon in two orthogonal transverse modes of
the waveguide. It is shown that by exploiting intermodal dispersion,
down-conversion into the relevant pairs of spatial modes can be selected by
spectral filtering, which also provides means to fine-tune the properties of
the generated entangled state. We also discuss an inverting interferometer
detecting the spatial parity of the input beam as a versatile tool to
characterize properties of the generated state. A single-photon Wigner function
obtained by a scan of the displaced parity can be used to identify the basis
modes of spatial qubit, whereas correlations between displaced parity
measurements on two photons can directly verify quantum entanglement through a
violation of Bell's inequalities.
