Proof of Heisenberg's error-disturbance relation

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dc.identifier.uri http://dx.doi.org/10.15488/8781
dc.identifier.uri https://www.repo.uni-hannover.de/handle/123456789/8834
dc.contributor.author Busch, Paul
dc.contributor.author Lahti,Pekka
dc.contributor.author Werner, Reinhard F.
dc.date.accessioned 2019-12-11T12:50:54Z
dc.date.available 2019-12-11T12:50:54Z
dc.date.issued 2013
dc.identifier.citation Busch, P.; Lahti, P.; Werner, R.F.: Proof of Heisenberg's error-disturbance relation. In: Physical Review Letters 111 (2013), Nr. 16, 160405. DOI: https://doi.org/10.1103/PhysRevLett.111.160405
dc.description.abstract While the slogan “no measurement without disturbance” has established itself under the name of the Heisenberg effect in the consciousness of the scientifically interested public, a precise statement of this fundamental feature of the quantum world has remained elusive, and serious attempts at rigorous formulations of it as a consequence of quantum theory have led to seemingly conflicting preliminary results. Here we show that despite recent claims to the contrary [L. Rozema et al, Phys. Rev. Lett. 109, 100404 (2012)], Heisenberg-type inequalities can be proven that describe a tradeoff between the precision of a position measurement and the necessary resulting disturbance of momentum (and vice versa). More generally, these inequalities are instances of an uncertainty relation for the imprecisions of any joint measurement of position and momentum. Measures of error and disturbance are here defined as figures of merit characteristic of measuring devices. As such they are state independent, each giving worst-case estimates across all states, in contrast to previous work that is concerned with the relationship between error and disturbance in an individual state.While the slogan “no measurement without disturbance” has established itself under the name of the Heisenberg effect in the consciousness of the scientifically interested public, a precise statement of this fundamental feature of the quantum world has remained elusive, and serious attempts at rigorous formulations of it as a consequence of quantum theory have led to seemingly conflicting preliminary results. Here we show that despite recent claims to the contrary [L. Rozema et al, Phys. Rev. Lett. 109, 100404 (2012)], Heisenberg-type inequalities can be proven that describe a tradeoff between the precision of a position measurement and the necessary resulting disturbance of momentum (and vice versa). More generally, these inequalities are instances of an uncertainty relation for the imprecisions of any joint measurement of position and momentum. Measures of error and disturbance are here defined as figures of merit characteristic of measuring devices. As such they are state independent, each giving worst-case estimates across all states, in contrast to previous work that is concerned with the relationship between error and disturbance in an individual state. eng
dc.language.iso eng
dc.publisher College Park, MD : American Physical Society
dc.relation.ispartofseries Physical Review Letters 111 (2013), Nr. 16
dc.rights Es gilt deutsches Urheberrecht. Das Dokument darf zum eigenen Gebrauch kostenfrei genutzt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.
dc.subject uncertainty relations eng
dc.subject.ddc 530 | Physik ger
dc.title Proof of Heisenberg's error-disturbance relation
dc.type article
dc.type Text
dc.relation.essn 1079-7114
dc.relation.issn 0031-9007
dc.relation.doi https://doi.org/10.1103/PhysRevLett.111.160405
dc.bibliographicCitation.issue 16
dc.bibliographicCitation.volume 111
dc.bibliographicCitation.firstPage 160405
dc.description.version publishedVersion
tib.accessRights frei zug�nglich


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