We propose two schemes for preparing four-photon cluster state through cross-Kerr nonlinearity.Twocoherent fields interact when they enter a nonlinear Kerr medium.If the interaction time is chosen appropriately ineach Kerr medium,four-photon cluster state can be generated based on the results of two homodyne detectors in thefirst scheme.These schemes only use Kerr medium and homodyne measurements on coherent light fields,which canbe efficiently made in quantum optical laboratories.In addition,weak cross-Kerr nonlinearity is sufficient.All of theproperties make these schemes feasible in experiments.
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