Implementation of a Nondeterministic Optical Noiseless Amplifier

Abstract

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 into 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 realisation 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 6dB gain and a noise level significantly smaller than the minimal allowed for any ordinary phase-independent device.Quantum optical detection techniques are so advanced that quantum fluctuations are the main source of noise. Therefore, when amplifying optical signals, one has to look at intrinsic limitations of the process: any amplifier cannot work independently on the phase of the input, unless some additional noise is added [1]. The origin of this limitation is that adding extra noise is needed for the output field to obey Heisenberg's uncertainty relation. Also, it is connected to the impossibility of realizing arbitrarily faithful copies of a quantum signal [2,3], and it is thus deeply rooted in the linear and unitary evolution of quantum mechanical systems.Various aspects of this limitation have been studied by using optical parametric amplifiers [4,5,6,7]. For instance, a non-degenerate optical parametric amplifier amplifies all input phases, and introduces the minimal level of added noise, which degrades the signal-to-noise ratio [1]. The same process, driven in the degenerate regime, may provide amplification preserving the signalto-noise ratio. However, this occurs in a phase-dependent fashion: only the part of the signal in phase with the pump light will be amplified, while the part which is 90 degrees out of phase with the pump will be deamplified [4,5].A more intriguing idea is to find a way to tamper with the linear evolution of quantum mechanics; this is actually possible, though non-deterministically, by conditioning our observation upon the result of a measurement [8]. Noiseless amplification can then take place, but only a fraction of the times, and the correct operation is heralded. This strategy is commonly adopted for building effective nonlinearities in linear quantum optical gates [9,10].Here we follow the proposal of Ralph and Lund [11] to demonstrate experimentally that heralded nondeterministic amplification can realise processes which would be impossible for usual amplifiers. Unlike another realisation [12], we have direct access to the output state via state tomography, so we can provide a complete description of the process, and analyse the limitations arising from non-ideal components. Our study is relevant in the long-term view of the integration of amplifiers in quantum communication lines [13].The conceptual layout of the noiseless amplifier...

Non-Gaussianity of quantum states: An experimental test on single-photon-added coherent states

“…Several implementations of non-Gaussian states have been reported so far, in particular from squeezed light [17][18][19][20][21][22][23][24][25], close-tothreshold parametric oscillators [26,27] in optical cavities [28], and in superconducting circuits [29]. Non-Gaussian operations are also interesting for tasks such as entanglement distillation [30,31] and noiseless amplification [32,33], which are also obtained in a conditional fashion, accepting only those events heralded by a measurement result.…”

Heralded processes on continuous-variable spaces as quantum maps

“…As an interesting feature, we are able to capture such nonclassical aspects at a glance. Our analysis first concerns the noiseless amplifier (Ĉ = gn, wherê n is the number operator and g > 1) [19,20]. We do not adopt a "black box" approach, but rather a model of the process is used so as to arrive at a description in term of generalized maps, also in the case when all the imperfections are taken into account.…”

“…[33]: its working principle is to use a nonmaximally entangled resource-a single photon split on an asymmetric beam splitter (A-BS)-to perform the teleportation of a coherent state |α . The analog of the Bell-state [19]. A single photon is conditionally generated upon detection of a single photon on detector D 0 .…”

“…Here we show, by a detailed physical model, the description of two conditioned processes which are relevant to continuous-variable state manipulation: the noiseless amplifier [19,20] and the single-photon addition [11,23]. We can derive the expression of the map in the well-known tensor form, and, as a step further, we illustrate a transfer function formalism, which allows us to describe the quantum process directly in the Wigner representation.…”

Thermal state truncation by using quantum-scissors device

“…Following these works on QSD, Ferreyrol et al implemented a nondeterministic optical noiseless amplifier for a coherent state [21]. Moreover, heralded noiseless linear amplifications were designed and realized [22][23][24].…”