Standard quantum limits of measurement error and methods of overcoming them

The so-called standard quantum limits (SQL) of measurement errors of coordinate, momentum, amplitude of oscillations, energy, force etc. are due to back action of the meter on the system under test, whenever the meter responds to the coordinate of the system. These SQL are not fundamental and can be surmounted by various methods. In particular, in a coordinate measurement the SQL can be overcome by means of an appropriate correlation of conjugate meter variables. Conditions of quantum nonperturbing (nondemolition) and quasi-nonperturbing measurements of the energy of electromagnetic waves are discussed. Possible methods of these measurements are reviewed. Conditions for overcoming the SQL of wave energy measurement by the optical Kerr effect are analysed. The quantum limit of error of this measurement is discussed. The effects of dissipation, dispersion and generation of combination waves are considered. Results of experiments reported in the literature are discussed. The dependence of the quantum limit of detection of an external action upon a system on the initial state of the system is considered. The relation between the measurement error of an observable A and a perturbation of an observable B, when [A,B] is an operator, is examined.