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...

We show that the maximum transmission distance of continuous-variable quantum key distribution in presence of a Gaussian noisy lossy channel can be arbitrarily increased using a heralded noiseless linear amplifier. We explicitly consider a protocol using amplitude-and phase-modulated coherent states with reverse reconciliation. Assuming that the secret key rate drops to zero for a line transmittance T lim , we find that a noiseless amplifier with amplitude gain g can improve this value to T lim /g 2 , corresponding to an increase in distance proportional to log g.