Engineering quantum operations is one of the main abilities we need for developing quantum technologies and designing new fundamental tests. Here we propose a scheme for realising a controlled operation acting on a travelling quantum field, whose fun
ctioning is determined by an input qubit. This study introduces new concepts and methods in the interface of continuous- and discrete-variable quantum optical systems.
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.
