OPTIMAL LARGE-SCALE QUANTUM STATE TOMOGRAPHY WITH PAULI MEASUREMENTS

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dc.contributor.authorCai, Tonyko
dc.contributor.authorKim, Donggyuko
dc.contributor.authorWang, Yazhenko
dc.contributor.authorYuan, Mingko
dc.contributor.authorZhou, Harrison H.ko
dc.date.accessioned2017-09-08T06:01:59Z-
dc.date.available2017-09-08T06:01:59Z-
dc.date.created2017-09-01-
dc.date.created2017-09-01-
dc.date.issued2016-04-
dc.identifier.citationANNALS OF STATISTICS, v.44, no.2, pp.682 - 712-
dc.identifier.issn0090-5364-
dc.identifier.urihttp://hdl.handle.net/10203/225857-
dc.description.abstractQuantum state tomography aims to determine the state of a quantum system as represented by a density matrix. It is a fundamental task in modern scientific studies involving quantum systems. In this paper, we study estimation of high-dimensional density matrices based on Pauli measurements. In particular, under appropriate notion of sparsity, we establish the minimax optimal rates of convergence for estimation of the density matrix under both the spectral and Frobenius norm losses; and show how these rates can be achieved by a common thresholding approach. Numerical performance of the proposed estimator is also investigated.-
dc.languageEnglish-
dc.publisherINST MATHEMATICAL STATISTICS-
dc.subjectHIGH-DIMENSIONAL MATRICES-
dc.subjectLOW-RANK MATRICES-
dc.subjectOPTIMAL RATES-
dc.subjectCOMPLETION-
dc.subjectPENALIZATION-
dc.subjectCONVERGENCE-
dc.subjectCOMPUTATION-
dc.subjectESTIMATORS-
dc.subjectSELECTION-
dc.subjectRECOVERY-
dc.titleOPTIMAL LARGE-SCALE QUANTUM STATE TOMOGRAPHY WITH PAULI MEASUREMENTS-
dc.typeArticle-
dc.identifier.wosid000372594300009-
dc.identifier.scopusid2-s2.0-84963686168-
dc.type.rimsART-
dc.citation.volume44-
dc.citation.issue2-
dc.citation.beginningpage682-
dc.citation.endingpage712-
dc.citation.publicationnameANNALS OF STATISTICS-
dc.identifier.doi10.1214/15-AOS1382-
dc.contributor.localauthorKim, Donggyu-
dc.contributor.nonIdAuthorCai, Tony-
dc.contributor.nonIdAuthorWang, Yazhen-
dc.contributor.nonIdAuthorYuan, Ming-
dc.contributor.nonIdAuthorZhou, Harrison H.-
dc.description.isOpenAccessN-
dc.type.journalArticleArticle-
dc.subject.keywordAuthorCompressed sensing-
dc.subject.keywordAuthordensity matrix-
dc.subject.keywordAuthorPauli matrices-
dc.subject.keywordAuthorquantum measurement-
dc.subject.keywordAuthorquantum probability-
dc.subject.keywordAuthorquantum statistics-
dc.subject.keywordAuthorsparse representation-
dc.subject.keywordAuthorspectral norm-
dc.subject.keywordAuthorminimax estimation-
dc.subject.keywordPlusHIGH-DIMENSIONAL MATRICES-
dc.subject.keywordPlusLOW-RANK MATRICES-
dc.subject.keywordPlusOPTIMAL RATES-
dc.subject.keywordPlusCOMPLETION-
dc.subject.keywordPlusPENALIZATION-
dc.subject.keywordPlusCONVERGENCE-
dc.subject.keywordPlusCOMPUTATION-
dc.subject.keywordPlusESTIMATORS-
dc.subject.keywordPlusSELECTION-
dc.subject.keywordPlusRECOVERY-
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