OPTIMAL LARGE-SCALE QUANTUM STATE TOMOGRAPHY WITH PAULI MEASUREMENTS

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Quantum 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.
Publisher
INST MATHEMATICAL STATISTICS
Issue Date
2016-04
Language
English
Article Type
Article
Keywords

HIGH-DIMENSIONAL MATRICES; LOW-RANK MATRICES; OPTIMAL RATES; COMPLETION; PENALIZATION; CONVERGENCE; COMPUTATION; ESTIMATORS; SELECTION; RECOVERY

Citation

ANNALS OF STATISTICS, v.44, no.2, pp.682 - 712

ISSN
0090-5364
DOI
10.1214/15-AOS1382
URI
http://hdl.handle.net/10203/225857
Appears in Collection
MT-Journal Papers(저널논문)
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