  Quantum optics dictates that amplification of a pure state by any linear
deterministic amplifier always introduces noise in the signal and results in a
mixed output state. However, it has recently been shown that noiseless
amplification becomes possible if the requirement of a deterministic operation
is relaxed. Here we propose and analyze a noiseless amplification scheme where
the energy required to amplify the signal originates from the stochastic
fluctuations in the field itself. In contrast to previous amplification setups,
our setup shows that a signal can be amplified even if no energy is added to
the signal from external sources. We investigate the relation between the
amplification and its success rate as well as the statistics of the output
states after successful and failed amplification processes. Furthermore, we
also optimize the setup to find the maximum success rates in terms of the
reflectivities of the beam splitters used in the setup and discuss the relation
of our setup with the previous setups.
