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dc.contributor.authorLounici, Karim
dc.contributor.authorMeziani, Katia
dc.contributor.authorPeyré, Gabriel
dc.date.accessioned2019-09-25T10:25:10Z
dc.date.available2019-09-25T10:25:10Z
dc.date.issued2018
dc.identifier.issn0090-5364
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/19916
dc.language.isoenen
dc.subjectL 2 and L∞ Risksen
dc.subjectIn-en
dc.subjectInverse problemen
dc.subjectNon-parametric minimax estimationen
dc.subjectAdaptive estimationen
dc.subjectQuantum homodyne tomographyen
dc.subjectWigner functionen
dc.subjectRadonen
dc.subjectRadon transformen
dc.subjectQuantum stateen
dc.subject.ddc519en
dc.titleAdaptive sup-norm estimation of the Wigner function in noisy quantum homodyne tomographyen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenIn quantum optics, the quantum state of a light beam is represented through the Wigner function, a density on R 2 which may take negative values but must respect intrinsic positivity constraints imposed by quantum physics. In the framework of noisy quantum homodyne tomography with efficiency parameter 1/2 < η ≤ 1, we study the theoretical performance of a kernel estimator of the Wigner function. We prove that it is minimax efficient, up to a logarithmic factor in the sample size, for the L∞-risk over a class of infinitely differentiable functions. We also compute the lower bound for the L 2-risk. We construct an adaptive estimator, i.e. which does not depend on the smoothness parameters, and prove that it attains the minimax rates for the corresponding smoothness of the class of functions up to a logarithmic factor in the sample size. Finite sample behaviour of our adaptive procedure is explored through numerical experiments.en
dc.relation.isversionofjnlnameThe Annals of Statistics
dc.relation.isversionofjnlvol46en
dc.relation.isversionofjnlissue3en
dc.relation.isversionofjnldate2018
dc.relation.isversionofjnlpages1318-1351.en
dc.relation.isversionofdoi10.1214/17-AOS1586en
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2019-09-25T10:17:12Z
hal.person.labIds7772
hal.person.labIds60
hal.person.labIds60$$$66


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