Proposed optical realisation of a two photon, four-qubit entangled χ state

The four-qubit states χ ij 〉 , exhibiting genuine 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 χ ij 〉 states. Our approach uses hyper-entangled photon pairs, produced by the type-I spontaneous parametric down-conversion 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. After one of these daughter photons passes through our optical setup, we obtain photon pairs in the hyper-entangled state χ 00 〉 , and the χ ij 〉 states can be achieved by further simple transformations.