Open Access
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

Inst. Math. Stat. (IMS) Collect., 2013: 213-226 (2013) DOI: 10.1214/12-IMSCOLL915


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.


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

zbMATH: 1327.62434
MathSciNet: MR3202635

Digital Object Identifier: 10.1214/12-IMSCOLL915

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

Back to Top