Generation of three-photon polarization-entangled decoherence-free states

We present a generation proposal of three-photon polarization-entangled decoherence-free states, which are immune to the collective decoherence. Based on weak cross-Kerr nonlinearities, the polarization and spacial entanglement gates are realized, and thus three-photon polarization-entangled decoherence-free states can be produced. According to the outcomes of Homodyne measurement performed in the spacial entanglement gate, one Swap gate is inserted into two paths of the photon 1 to swap its spacial modes, by means of classical feed forward. In addition, in the process for realizing two entanglement gates, unitary transformation operations are performed on the appropriate photons conditioned on the different phase shifts occurred on the coherent states, aiming to obtain the same state under two scenarios of the different path compositions of photons. At the output ports of the circuit, three-photon polarization-entangled decoherence-free states which can be utilized to represent two logical qubits, |0〉L|0〉L and |1〉L|1〉L are achieved. Apart from Kerr media, only simple linear optical elements and the classical feed forward techniques are necessary in this proposal, facilitating its practical implementation.