  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.
