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VOL. 9 | 2013 A remark on low rank matrix recovery and noncommutative Bernstein type inequalities
Vladimir Koltchinskii

Editor(s) M. Banerjee, F. Bunea, J. Huang, V. Koltchinskii, M. H. Maathuis

Abstract

A problem of estimation of a large Hermitian nonnegatively definite matrix of trace 1 (a density matrix of a quantum system) motivated by quantum state tomography is studied. The estimator is based on a modified least squares method suitable in the case of models with random design with known design distributions. The bounds on Hilbert-Schmidt error of the estimator, including low rank oracle inequalities, have been proved. The proofs rely on Bernstein type inequalities for sums of independent random matrices.

Information

Published: 1 January 2013
First available in Project Euclid: 8 March 2013

zbMATH: 1327.62434
MathSciNet: MR3202635

Digital Object Identifier: 10.1214/12-IMSCOLL915

Subjects:
Primary: 62J99
Secondary: 62H12, 60B20, 60G15

Keywords: low rank matrix estimation , matrix regression , noncommutative Bernstein inequality , quantum state tomography

Rights: Copyright © 2010, Institute of Mathematical Statistics

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