Entanglement concentration for six-particle cluster states

Multi-particle cluster states play a significant role in quantum information processing. However, due to the inevitable interaction with the environment in the transmission process, the fidelity of entanglement decreases. To distill the perfect cluster states, we present two schemes for arbitrary six-particle cluster states. POVM local unitary operators that are obtained by solving the equation according to the properties of cluster states are used in the first protocol. The second protocol is based on cross-Kerr nonlinearity which is exploited to check parity between original qubit with ancillary single qubit and it can achieve a higher probability of success through iteration. Furthermore, we can generalize the first method to concentrate entanglement on even number of particles. Our protocol will be useful in practical applications.