Uncertainty relation and the measurement error-perturbation relation

Lomonosov Moscow State University, Department of Physics, Vorobevy gory, Moscow, 119992, 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.

Text can be downloaded in Russian. English translation is available on IOP Science.
PACS: 03.65.−w, 03.65.Ta, 03.67.−a (all)
DOI: 10.1070/PU2005v048n10ABEH005794
Citation: Vorontsov Yu I "Uncertainty relation and the measurement error-perturbation relation" Phys. Usp. 48 999–1013 (2005)
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Оригинал: Воронцов Ю И «Соотношение неопределенности и соотношение ошибка измерения-возмущение» УФН 175 1053–1068 (2005); DOI: 10.3367/UFNr.0175.200510f.1053

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