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 times, the ECP has the approximate maximal success probability 100 %. Moreover, the present protocol is also suitable for partially entangled -photon cluster states concentration. All these advantages make this protocol more efficient and more convenient than others in the applications in quantum communication.