dc.contributor.author
Carpentier, Alexandra
dc.contributor.author
Eisert, Jens
dc.contributor.author
Gross, David
dc.contributor.author
Nickl, Richard
dc.date.accessioned
2020-12-01T12:11:43Z
dc.date.available
2020-12-01T12:11:43Z
dc.identifier.uri
https://refubium.fu-berlin.de/handle/fub188/27364
dc.identifier.uri
http://dx.doi.org/10.17169/refubium-27120
dc.description.abstract
We construct minimax optimal non-asymptotic confidence sets for low rank matrix recovery algorithms such as the Matrix Lasso or Dantzig selector. These are employed to devise adaptive sequential sampling procedures that guarantee recovery of the true matrix in Frobenius norm after a data-driven stopping time n^ for the number of measurements that have to be taken. With high probability, this stopping time is minimax optimal. We detail applications to quantum tomography problems where measurements arise from Pauli observables. We also give a theoretical construction of a confidence set for the density matrix of a quantum state that has optimal diameter in nuclear norm. The non-asymptotic properties of our confidence sets are further investigated in a simulation study.
en
dc.format.extent
37 Seiten
dc.rights.uri
http://www.fu-berlin.de/sites/refubium/rechtliches/Nutzungsbedingungen
dc.subject
low rank recovery
en
dc.subject
quantum information
en
dc.subject
confidence sets
en
dc.subject
sequential sampling
en
dc.subject.ddc
500 Naturwissenschaften und Mathematik::530 Physik::530 Physik
dc.title
Uncertainty quantification for matrix compressed sensing and quantum tomography problems
dc.type
Konferenzveröffentlichung
dcterms.bibliographicCitation.editor
Nathael Gozlan, Rafał Latała, Karim Lounici, Mokshay Madiman (Eds.)
dcterms.bibliographicCitation.originalpublishername
Birkhäuser
dcterms.bibliographicCitation.originalpublisherplace
Cham
dcterms.bibliographicCitation.pagestart
385
dcterms.bibliographicCitation.pageend
430
dcterms.bibliographicCitation.url
https://doi.org/10.1007/978-3-030-26391-1_18
refubium.affiliation
Physik
refubium.resourceType.isindependentpub
no
dcterms.accessRights.openaire
open access
dcterms.isPartOf.isbn
978-3-030-26390-4
dcterms.isPartOf.eisbn
978-3-030-26391-1