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Schemes for quantum entanglement concentration of two unknown partially entangled states with cross-Kerr nonlinearity

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 the 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 state with a certain success probability. Finally, we discuss the influences of sources of errors and decoherence on the schemes. The proposed setup is very simple, just employing some linear optical elements and cross-Kerr medium, which greatly simplifies the experimental realization of the schemes. The schemes are feasible within current experimental technology