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Laser Physics Letters

Nondeterministic noiseless amplification of optical signals: a review of recent experiments

Marco Barbieri, Franck Ferreyrol, Rémi Blandino, Rosa Tualle-Brouri, Philippe Grangier

Published Apr 5, 2011• 39 citations
Publisher

Abstract

Linear amplifiers necessarily introduce a minimal amount of noise, as required by Heisenberg's relation in quantum mechanics. Such a limitation could be overcome when considering nondeterminsitic processes, heralded by a trigger event. Here we present a review of implementations of this technique, which have recently appeared in the literature.

DOI
10.1002/lapl.201010143

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Linear amplifiers necessarily introduce a minimal amount of noise, as required by Heisenberg's relation in quantum mechanics. Such a limitation could be overcome when considering nondeterminsitic processes, heralded by a trigger event. Here we present a review of implementations of this technique, which have recently appeared in the literature.
Linear amplifiers are necessarily affected by a minimal amount of noise, which is needed in order to preserve the linearity and the unitarity prescribed by quantum mechanics. Such a limitation might be partially overcome if the process is realized by conditioning its operation on a trigger event, for instance, the result of a measurement. Here we present a detailed analysis of a noiseless amplifier, implemented using linear optics, a down-conversion-based single-photon source, and single-photon detection. Our results demonstrate an amplification adding a level of noise lower than the minimum allowed by quantum mechanics for deterministic amplifiers. This is made possible by the nondeterministic character of our device, whose success rate is sufficiently low not to violate any fundamental limit. We compare our experimental data to a model taking into account the main imperfections of the setup and find a good agreement.
According to the fundamental laws of quantum optics, noise is necessarily added to the system when one tries to clone or amplify a quantum state. However, it has recently been shown that the quantum noise related to the operation of a linear phase-insensitive amplifier can be avoided when the requirement of a deterministic operation is relaxed. Nondeterministic noiseless linear amplifiers are therefore realizable. Usually nondeterministic amplifiers rely on using single photon sources. We have, in contrast, recently proposed an amplification scheme in which no external energy is added to the signal, but the energy required to amplify the signal originates from the stochastic fluctuations in the field itself. Applying our amplification scheme, we examine the amplifier gain and the success rate as well as the properties of the output states after successful and failed amplification processes. We also optimize the setup to find the maximum success rates in terms of the reflectivities of the beam splitters used in the setup. In addition, we discuss the nonidealities related to the operation of our setup and the relation of our setup with the previous setups.
According to the fundamental laws of quantum optics, noise is necessarily added to the system when one tries to clone or amplify a quantum state. However, it has recently been shown that the quantum noise related to the operation of a linear phase-insensitive amplifier can be avoided when the requirement of a deterministic op-eration is relaxed. Nondeterministic noiseless linear amplifiers are therefore realizable. Usually nondeterministic amplifiers rely on using single photon sources. We have, in contrast, recently proposed an amplification scheme in which no external energy is added to the signal, but the energy required to amplify the signal originates from the stochastic fluctuations in the field itself. Applying our amplification scheme, we examine the amplifier gain and the success rate as well as the properties of the output states after successful and failed amplification processes. We also optimize the setup to find the maximum success rates in terms of the reflectivities of the beam splitters used in the setup. In addition, we discuss the nonidealities related to the operation of our setup and the relation of our setup with the previous setups.
Quantum mechanics imposes that any amplifier that works independently on the phase of the input signal has to introduce some excess noise. The impossibility of such a noiseless amplifier is rooted in the unitarity and linearity of quantum evolution. A possible way to circumvent this limitation is to interrupt such evolution via a measurement, providing a random outcome able to herald a successful-and noiseless-amplification event. Here we show a successful realization of such an approach; we perform a full characterization of an amplified coherent state using quantum homodyne tomography, and observe a strong heralded amplification, with about a 6 dB gain and a noise level significantly smaller than the minimal allowed for any ordinary phase-independent device.