We propose practical schemes for concentrating entanglement of a pair of unknown partially entangled Bell states and three-photon W states with cross-Kerr nonlinearity. In these schemes, utilizing local operations and classical communication, two separated parties can obtain one maximally entangled photon pair from two previously shared partially entangled photon pairs, and three separated parties can obtain one maximally entangled three-photon W state and a maximally entangled cluster state from two identical partially entangled three-photon W states with a certain success probability. Finally, we discuss the influence of sources of error and decoherence on the schemes. The proposed setup only employs some linear optical elements and the cross-Kerr medium, which greatly reduces the difficulty of experimental realization. These schemes are feasible with current experimental technology.
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