Heisenberg uncertainty for qubit measurements

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dc.identifier.uri http://dx.doi.org/10.15488/8777
dc.identifier.uri https://www.repo.uni-hannover.de/handle/123456789/8830
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 2014
dc.identifier.citation Busch, P.; Lahti, P.; Werner, R.F.: Heisenberg uncertainty for qubit measurements. In: Physical Review A 89 (2014), Nr. 1, 012129. DOI: https://doi.org/10.1103/PhysRevA.89.012129
dc.description.abstract Reports on experiments recently performed in Vienna [Erhard et al., Nature Phys. 8, 185 (2012)] and Toronto [Rozema et al., Phys. Rev. Lett. 109, 100404 (2012)] include claims of a violation of Heisenberg's error-disturbance relation. In contrast, we have presented and proven a Heisenberg-type relation for joint measurements of position and momentum [Phys. Rev. Lett. 111, 160405 (2013)]. To resolve the apparent conflict, we formulate here a general trade-off relation for errors in qubit measurements, using the same concepts as we did in the position-momentum case. We show that the combined errors in an approximate joint measurement of a pair of ±1-valued observables A,B are tightly bounded from below by a quantity that measures the degree of incompatibility of A and B. The claim of a violation of Heisenberg is shown to fail because it is based on unsuitable measures of error and disturbance. Finally we show how the experiments mentioned may directly be used to test our error inequality.Reports on experiments recently performed in Vienna [Erhard et al., Nature Phys. 8, 185 (2012)] and Toronto [Rozema et al., Phys. Rev. Lett. 109, 100404 (2012)] include claims of a violation of Heisenberg's error-disturbance relation. In contrast, we have presented and proven a Heisenberg-type relation for joint measurements of position and momentum [Phys. Rev. Lett. 111, 160405 (2013)]. To resolve the apparent conflict, we formulate here a general trade-off relation for errors in qubit measurements, using the same concepts as we did in the position-momentum case. We show that the combined errors in an approximate joint measurement of a pair of ±1-valued observables A,B are tightly bounded from below by a quantity that measures the degree of incompatibility of A and B. The claim of a violation of Heisenberg is shown to fail because it is based on unsuitable measures of error and disturbance. Finally we show how the experiments mentioned may directly be used to test our error inequality. eng
dc.language.iso eng
dc.publisher College Park, MD : American Physical Society
dc.relation.ispartofseries Physical Review A 89 (2014), Nr. 1
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 quantum mechanics eng
dc.subject Heisenberg relation eng
dc.subject Ozawa inequality eng
dc.subject.ddc 530 | Physik ger
dc.title Heisenberg uncertainty for qubit measurements
dc.type article
dc.type Text
dc.relation.essn 1094-1622
dc.relation.essn 2469-9926
dc.relation.essn 2469-9934
dc.relation.issn 0556-2791
dc.relation.issn 1050-2947
dc.relation.doi https://doi.org/10.1103/PhysRevA.89.012129
dc.bibliographicCitation.issue 1
dc.bibliographicCitation.volume 89
dc.bibliographicCitation.firstPage 12129
dc.description.version publishedVersion
tib.accessRights frei zug�nglich


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