Measurement Uncertainty for Finite Quantum Observables

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dc.identifier.uri http://dx.doi.org/10.15488/1584
dc.identifier.uri http://www.repo.uni-hannover.de/handle/123456789/1609
dc.contributor.author Schwonnek, René
dc.contributor.author Reeb, David
dc.contributor.author Werner, Reinhard F.
dc.date.accessioned 2017-05-31T11:16:23Z
dc.date.available 2017-05-31T11:16:23Z
dc.date.issued 2016
dc.identifier.citation Schwonnek, René; Reeb, David; Werner, Reinhard: Measurement Uncertainty for Finite Quantum Observables. In: Mathematics 4 (2016), Nr. 2, 38. DOI: https://doi.org/10.3390/math4020038
dc.description.abstract Measurement uncertainty relations are lower bounds on the errors of any approximate joint measurement of two or more quantum observables. The aim of this paper is to provide methods to compute optimal bounds of this type. The basic method is semidefinite programming, which we apply to arbitrary finite collections of projective observables on a finite dimensional Hilbert space. The quantification of errors is based on an arbitrary cost function, which assigns a penalty to getting result x rather than y, for any pair (x,y) . This induces a notion of optimal transport cost for a pair of probability distributions, and we include an Appendix with a short summary of optimal transport theory as needed in our context. There are then different ways to form an overall figure of merit from the comparison of distributions. We consider three, which are related to different physical testing scenarios. The most thorough test compares the transport distances between the marginals of a joint measurement and the reference observables for every input state. Less demanding is a test just on the states for which a “true value” is known in the sense that the reference observable yields a definite outcome. Finally, we can measure a deviation as a single expectation value by comparing the two observables on the two parts of a maximally-entangled state. All three error quantities have the property that they vanish if and only if the tested observable is equal to the reference. The theory is illustrated with some characteristic examples. eng
dc.description.sponsorship BMBF/Q.com-Q
dc.description.sponsorship DFG/WE1240/20
dc.description.sponsorship DQSIM
dc.description.sponsorship SIQS
dc.language.iso eng
dc.publisher Basel : MDPI AG
dc.relation.ispartofseries Mathematics 4 (2016), Nr. 2
dc.rights CC BY 4.0 Unported
dc.rights.uri https://creativecommons.org/licenses/by/4.0/
dc.subject error-disturbance tradeoff eng
dc.subject measurement uncertainty eng
dc.subject optimal transport eng
dc.subject semidefinite programming eng
dc.subject uncertainty relations eng
dc.subject.ddc 510 | Mathematik ger
dc.title Measurement Uncertainty for Finite Quantum Observables
dc.type article
dc.type Text
dc.relation.issn 2227-7390
dc.relation.doi https://doi.org/10.3390/math4020038
dc.bibliographicCitation.issue 2
dc.bibliographicCitation.volume 4
dc.bibliographicCitation.firstPage 38
dc.description.version publishedVersion
tib.accessRights frei zug�nglich


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