Show simple item record

dc.contributor.authorLounici, Karim*
dc.contributor.authorMeziani, Katia*
dc.contributor.authorPeyré, Gabriel*
dc.date.accessioned2017-12-07T11:01:45Z
dc.date.available2017-12-07T11:01:45Z
dc.date.issued2018
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17194
dc.language.isoenen
dc.subjectL 2 and L∞ Risks
dc.subjectIn-
dc.subjectInverse problem
dc.subjectNon-parametric minimax estimation
dc.subjectAdaptive estimation
dc.subjectQuantum homodyne tomography
dc.subjectWigner function
dc.subjectRadon
dc.subjectRadon transform
dc.subjectQuantum state
dc.subject.ddc519en
dc.titleAdaptive sup-norm estimation of the Wigner function in noisy quantum homodyne tomography
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.
dc.relation.isversionofjnlnameThe Annals of Statistics
dc.relation.isversionofjnlvol46
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2018
dc.relation.isversionofjnlpages1318-1351
dc.relation.isversionofdoi10.1214/17-AOS1586
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01491197
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.date.updated2017-12-15T17:23:53Z
hal.person.labIds*
hal.person.labIds*
hal.person.labIds*


Files in this item

FilesSizeFormatView

There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record