  Quantum key distribution establishes a secret string of bits between two
distant parties. Of concern in weak laser pulse schemes is the especially
strong photon number splitting attack by an eavesdropper, but the decoy state
method can detect this attack with current technology, yielding a high rate of
secret bits. In this Letter, we develop rigorous security statements in the
case of finite statistics with only a few decoy states, and we present the
results of simulations of an experimental setup of a decoy state protocol that
can be simply realized with current technology.
