Accurate quantum nondemolition measurements of optical solitons

A fully quantum- mechanical Heisenberg description of the quantum-nondemolition measurements via soliton collision in an optical fiber is provided. Solutions to the equations of motion for meaningful soliton collective operators such as photon number, phase, position, and frequency (momentum) are applied to quantifying the error of inference of photon number and frequency of the signal soliton by performing a measurement on the probe soliton. A detection method based on measuring a four-component quadrature amplitude is proposed and proved to give the best accuracy.