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Article: Attaining the Ultimate Precision Limit in Quantum State Estimation

TitleAttaining the Ultimate Precision Limit in Quantum State Estimation
Authors
Issue Date2019
PublisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00220/index.htm
Citation
Communications in Mathematical Physics, 2019, v. 368 n. 1, p. 223-293 How to Cite?
AbstractWe derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic covariance, which is weaker than unbiasedness or local unbiasedness. The derivation is based on an analysis of the limiting distribution of the estimator’s deviation from the true value of the parameter, and takes advantage of quantum local asymptotic normality, a useful asymptotic characterization of identically prepared states in terms of Gaussian states. We first prove our results for the mean square error of a special class of models, called D-invariant, and then extend the results to arbitrary models, generic cost functions, and global state estimation, where the unknown parameter is not restricted to a local neighbourhood of the true value. The extension includes a treatment of nuisance parameters, i.e. parameters that are not of interest to the experimenter but nevertheless affect the precision of the estimation. As an illustration of the general approach, we provide the optimal estimation strategies for the joint measurement of two qubit observables, for the estimation of qubit states in the presence of amplitude damping noise, and for noisy multiphase estimation.
Persistent Identifierhttp://hdl.handle.net/10722/270125
ISSN
2023 Impact Factor: 2.2
2023 SCImago Journal Rankings: 1.612
ISI Accession Number ID
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DC FieldValueLanguage
dc.contributor.authorYang, Y-
dc.contributor.authorChiribella, G-
dc.contributor.authorHayashi, M-
dc.date.accessioned2019-05-20T05:10:05Z-
dc.date.available2019-05-20T05:10:05Z-
dc.date.issued2019-
dc.identifier.citationCommunications in Mathematical Physics, 2019, v. 368 n. 1, p. 223-293-
dc.identifier.issn0010-3616-
dc.identifier.urihttp://hdl.handle.net/10722/270125-
dc.description.abstractWe derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non-degenerate. Our results hold under an assumption called local asymptotic covariance, which is weaker than unbiasedness or local unbiasedness. The derivation is based on an analysis of the limiting distribution of the estimator’s deviation from the true value of the parameter, and takes advantage of quantum local asymptotic normality, a useful asymptotic characterization of identically prepared states in terms of Gaussian states. We first prove our results for the mean square error of a special class of models, called D-invariant, and then extend the results to arbitrary models, generic cost functions, and global state estimation, where the unknown parameter is not restricted to a local neighbourhood of the true value. The extension includes a treatment of nuisance parameters, i.e. parameters that are not of interest to the experimenter but nevertheless affect the precision of the estimation. As an illustration of the general approach, we provide the optimal estimation strategies for the joint measurement of two qubit observables, for the estimation of qubit states in the presence of amplitude damping noise, and for noisy multiphase estimation.-
dc.languageeng-
dc.publisherSpringer Verlag. The Journal's web site is located at http://link.springer.de/link/service/journals/00220/index.htm-
dc.relation.ispartofCommunications in Mathematical Physics-
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.titleAttaining the Ultimate Precision Limit in Quantum State Estimation-
dc.typeArticle-
dc.identifier.emailChiribella, G: giulio@hku.hk-
dc.identifier.authorityChiribella, G=rp02035-
dc.description.naturepublished_or_final_version-
dc.identifier.doi10.1007/s00220-019-03433-4-
dc.identifier.scopuseid_2-s2.0-85065201540-
dc.identifier.hkuros297841-
dc.identifier.volume368-
dc.identifier.issue1-
dc.identifier.spage223-
dc.identifier.epage293-
dc.identifier.isiWOS:000467040500006-
dc.publisher.placeGermany-
dc.relation.projectCompressed Quantum Dynamics: Storing, Programming, and Simulating Physical Processes with Minimum-Sized Quantum Systems-
dc.identifier.issnl0010-3616-

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