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Physical Review A

Experimental realization of a nondeterministic optical noiseless amplifier

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

Published Jun 1, 2011• 56 citations
Publisher

Abstract

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.

DOI
10.1103/physreva.83.063801

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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.
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.
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.
Abstract We address the characterisation of non-deterministic noiseless linear amplifiers (NLAs) and compare the performances of different estimation strategies. In particular, we focus on estimation of the gain, whose value may result from a combination of different experimental effects, as those governing the overall efficiency of the detector or the transmissivity of the involved optical components. At first, we show that, contrary to naive expectations, post-selecting only the amplified states does not offer the most accurate estimate. We then focus on minimal implementations of a NLA, i.e. those obtained by coupling the input state to a two-level system, and show that the maximal amount of information about the gain of the NLA is obtained by measuring the whole composite system. The quantum Fisher information (QFI) of this best-case scenario is analysed in some detail, and compared to the QFI of the post-selected states, both for successful and unsuccessful amplification. Eventually, we show that full extraction of the available information is achieved when the non-deterministic process is implemented by a Lüders instrument. We also analyse the precision attainable by probing NLAs by single-mode pure states and measuring the field or the number of quanta, and discuss in some detail the specific cases of squeezed vacuum and coherent states.
Fundamental laws of quantum mechanics impose that arbitrary quantum states cannot be perfectly cloned or amplified without introducing some unavoidable noise in the process. The quantum noise intrinsic to the functioning of a linear phase-insensitive amplifier can however be avoided by relaxing the requirement of a deterministic operation. Non-deterministic noiseless linear amplifiers that do not violate any fundamental quantum law are therefore possible and here we present the first experimental realization of a scheme that allows noiseless amplification of coherent states at the best level of effective gain and final state fidelity ever reached. This scheme, based on a sequence of photon addition and subtraction, and characterized by a significant amplification and low distortions, may become a useful tool for quantum communications and metrology, by enhancing the discrimination between partially overlapping quantum states or by recovering the information transmitted over lossy channels.