Decoy states for quantum key distribution based on decoherence-free subspaces

Quantum key distribution with decoherence-free subspaces has been proposed to overcome the collective noise to the polarization modes of photons flying in quantum channel. Prototype of this scheme have also been achieved with parametric-down conversion source. However, a novel type of photon-number-splitting attack we proposed in this paper will make the practical implementations of this scheme insecure since the parametric-down conversion source may emit multi-photon pairs occasionally. We propose decoy states method to make these implementations immune to this attack. And with this decoy states method, both the security distance and key bit rate will be increased.