The security of decoy state protocol in the partial photon number splitting attack

The decoy state protocol was proposed to overcome the primitive photon number splitting attack. When using a better strategy, the attacker can ensure that the ratio of the overall gain of the signal state pulse against the decoy state pulse changes very little, even to keep the overall gain of the signal state pulses equal to that obtained without attacker. In this paper we first give a model of the partial photon number splitting attack which contains the original one, and then find that the decoy state protocol still works effectively under the partial photon number splitting attack.