  The four-qubit states $\lvert\chi^{ij}\rangle$, exhibiting genuinely
multi-partite entanglement have been shown to have many interesting properties
and have been suggested for novel applications in quantum information
processing. In this work we propose a simple quantum circuit and its
corresponding optical embodiment with which to prepare photon pairs in the
$\lvert\chi^{ij}\rangle$ states. Our approach uses hyper-entangled photon
pairs, produced by the type-I spontaneous parametric down-conversion (SPDC)
process in two contiguous nonlinear crystals, together with a set of simple
linear-optical transformations. Our photon pairs are maximally hyper-entangled
in both their polarisation and orbital angular momentum (OAM). After one of
these daughter photons passes through our optical setup, we obtain photon pairs
in the hyper-entangled state $\lvert\chi^{00}\rangle$, and the
$\lvert\chi^{ij}\rangle$ states can be achieved by further simple
transformations.
