Uncertainty relation and the measurement error-perturbation relation
Lomonosov Moscow State University, Department of Physics, Leninskie Gory 1 build. 2, Moscow, 119991, Russian Federation
The origins and physical consequences of the traditionally used relation between the position measurement error
and the momentum perturbation, Δ2mxΔ2ρp ≥ ħ2/4 are discussed. It is demonstrated that the corresponding increase in the momentum variance for the aposteriori state occurs only in
some special cases. The product of Δ2mA and Δ2ρB is shown to
essentially differ from the one given by the uncertainty relation if the commutator [Â, B] is an operator. The error quantum
limits for the joint homodyne measurement of quadrature amplitudes for an optical mode are found. It is shown that similar
results can be obtained if the quadratures of a harmonic oscillator are estimated by means of continuous position measurement.