Single logical qubit information encoding scheme with the minimal optical decoherence-free subsystem

We present a scheme for encoding single logical qubit information, which is immune to collective decoherence acting on Hilbert space spanned by the corresponding states. The scheme needs a spatial entanglement gate and a polarization entanglement gate, which are realized with the assistance of weak cross-Kerr nonlinear interaction between photons and coherent states via Kerr media. Under the condition of sufficient large phase shifts, single logical qubit information can be encoded into this minimal optical decoherence-free subsystem with near-unity fidelity. Together with the mature techniques of measurement and classical feed forward, simple linear optical elements are applied to complete the encoding task, which offers the feasibility of this scheme for protecting quantum information against decoherence.