Generation of an arbitrary four-photon polarization-entangled decoherence-free state with cross-Kerr nonlinearity

We present a new scheme to provide an arbitrary four-photon polarization-entangled state, which enables the encoding of single logical qubit information into a four-qubit decoherence-free subspace robustly against collective decoherence. With the assistance of the cross-Kerr nonlinearities, a spatial entanglement gate and a polarization entanglement gate are inserted into the circuit, where the X-quadrature homodyne measurement is properly performed. According to the outcomes of homodyne measurement in the spatial entanglement process, some swap gates are inserted into the corresponding paths of the photons to swap their spatial modes. Apart from Kerr media, some basic linear optical elements are necessary, which make it feasible with current experimental techniques.

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