Efficient entanglement concentration for partially entangled cluster states with weak cross-Kerr nonlinearity

In this paper, we propose an optimal entanglement concentration protocol (ECP) for partially entangled cluster states with the help of the weak cross-Kerr nonlinearity. We can obtain the maximally entangled cluster states assisted with the projection measurements on the additional photons. The protocol is based on optical elements, single polarization photons, cross-Kerr nonlinearity, and the conventional photon detectors, which are feasible with existing experimental technology. Numerical simulation demonstrates that by iterating the entanglement concentration process n=m=6 times, the ECP has the approximate maximal success probability 100 %. Moreover, the present protocol is also suitable for partially entangled 4N-photon cluster states concentration. All these advantages make this protocol more efficient and more convenient than others in the applications in quantum communication.