Optimal Large-Scale Quantum State Tomography With Pauli Measurements

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dc.contributor.authorCai, Tony
dc.contributor.authorKim, Donggyu
dc.contributor.authorWang, Yazhen
dc.contributor.authorYuan, Ming
dc.contributor.authorZhou, Harrison H
dc.date2023-05-17T17:47:53.000
dc.date.accessioned2023-05-23T03:38:35Z
dc.date.available2023-05-23T03:38:35Z
dc.date.issued2016-01-01
dc.date.submitted2017-08-21T11:11:57-07:00
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.identifier.urihttps://repository.upenn.edu/handle/20.500.14332/48088
dc.legacy.articleid1523
dc.legacy.fields10.1214/15-AOS1382
dc.legacy.fulltexturlhttps://repository.upenn.edu/cgi/viewcontent.cgi?article=1523&context=statistics_papers&unstamped=1
dc.rightsThe original and published work is available at: https://projecteuclid.org/euclid.aos/1458245732#abstract
dc.source.beginpage682
dc.source.endpage712
dc.source.issue81
dc.source.issue2
dc.source.journalStatistics Papers
dc.source.journaltitleThe Annals of Statistics
dc.source.peerreviewedtrue
dc.source.statuspublished
dc.source.volume44
dc.subject.otherCompressed sensing
dc.subject.otherdensity matrix
dc.subject.otherPauli matrices
dc.subject.otherquantum measurement
dc.subject.otherquantum probability
dc.subject.otherquantum statistics
dc.subject.othersparse representation
dc.subject.otherspectral norm
dc.subject.otherminimax estimation
dc.subject.otherPhysical Sciences and Mathematics
dc.titleOptimal Large-Scale Quantum State Tomography With Pauli Measurements
dc.typeArticle
digcom.identifierstatistics_papers/81
digcom.identifier.contextkey10633501
digcom.identifier.submissionpathstatistics_papers/81
digcom.typearticle
dspace.entity.typePublication
upenn.schoolDepartmentCenterStatistics Papers
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