  In the decoy quantum key distribution, we show that a smaller decoy intensity
gives a better key generation rate in the asymptotic setting when we employ
only one decoy intensity and the vacuum pulse. In particular, the counting rate
of single photon can be perfectly estimated when the decoy intensity is
infinitesimal. The same property holds even when the intensities cannot be
perfectly identified. Further, we propose a protocol to improve the key
generation rate over the existing protocol under the same decoy intensity.
