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 harmoni
c 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-determinist
