  A universal deterministic noiseless quantum amplifier has been shown to be
impossible. However, probabilistic noiseless amplification of a certain set of
states is physically permissible. Regarding quantum state amplification as
quantum state transformation, we show that deterministic noiseless
amplification of coherent states chosen from a proper set is possible. The
relation between input coherent states and gain of amplification for
deterministic noiseless amplification is thus derived. Besides, the potential
applications of amplification of coherent states in quantum key distribution
(QKD), noisy channel and non-ideal detection are also discussed.
