  The idea of signal amplification is ubiquitous in the control of physical
systems, and the ultimate performance limit of amplifiers is set by quantum
physics. Increasing the amplitude of an unknown quantum optical field, or more
generally any harmonic oscillator state, must introduce noise. This linear
amplification noise prevents the perfect copying of the quantum state, enforces
quantum limits on communications and metrology, and is the physical mechanism
that prevents the increase of entanglement via local operations. It is known
that non-deterministic versions of ideal cloning and local entanglement
increase (distillation) are allowed, suggesting the possibility of
non-deterministic noiseless linear amplification. Here we introduce, and
experimentally demonstrate, such a noiseless linear amplifier for
continuous-variables states of the optical field, and use it to demonstrate
entanglement distillation of field-mode entanglement. This simple but powerful
circuit can form the basis of practical devices for enhancing quantum
technologies. The idea of noiseless amplification unifies approaches to cloning
and distillation, and will find applications in quantum metrology and
communications.
