Abstract: 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. Usually, nondeterministic amplifiers rely on using single photon
sources. In contrast, we propose a noiseless amplification
scheme where the energy required to amplify the signal originates from the
stochastic fluctuations in the initial field itself. The proposed scheme
consists of devices that are generally used in quantum optical experiments
i.e. beam splitters, photodetectors, and a quantum nondemolition (QND)
measurement apparatus. A
QND measurement utilizes the energy fluctuations of the initial field to
replace the single photon source that would otherwise be needed as in the
scheme suggested by Zavatta et al. [Nature Photonics, vol. 5,
pp. 52-56, 2011]. The operation of our proposed amplifier is shortly
described as follows: first a single photon is subtracted from the initial
field by a beam splitter and it is verified using a QND measurement
apparatus. Second, the subtracted photon is added back to the field by a
beam splitter and a photodetector. Finally, another photon is subtracted
from the field using a beam splitter and a conventional
photodetector. The resulting output field is an amplified coherent field
with high fidelity. We apply the Wigner function formalism to analyze our
noiseless amplification scheme and to 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 previously reported setups. In addition,
the states after failed amplification are examined and the possibility of
repeated amplification process is discussed.
