The origins and physical consequences of the traditionally used relation between the position measurement error and the momentum perturbation, Δ²_mxΔ²_ρp ≥ 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 Δ²_mA and Δ²_ρB 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.

PACS: 03.65.−w, 03.65.Ta, 03.67.−a (all) DOI: 10.1070/PU2005v048n10ABEH005794 URL: https://ufn.ru/en/articles/2005/10/b/ 000235238900002 Citation: Vorontsov Yu I "Uncertainty relation and the measurement error-perturbation relation" Phys. Usp. 48 999–1013 (2005) BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks Оригинал: Воронцов Ю И «Соотношение неопределенности и соотношение ошибка измерения-возмущение» УФН 175 1053–1068 (2005); DOI: 10.3367/UFNr.0175.200510f.1053