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April 2016 Optimal large-scale quantum state tomography with Pauli measurements
Tony Cai, Donggyu Kim, Yazhen Wang, Ming Yuan, Harrison H. Zhou
Ann. Statist. 44(2): 682-712 (April 2016). DOI: 10.1214/15-AOS1382

Abstract

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.

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Tony Cai. Donggyu Kim. Yazhen Wang. Ming Yuan. Harrison H. Zhou. "Optimal large-scale quantum state tomography with Pauli measurements." Ann. Statist. 44 (2) 682 - 712, April 2016. https://doi.org/10.1214/15-AOS1382

Information

Received: 1 January 2015; Revised: 1 August 2015; Published: April 2016
First available in Project Euclid: 17 March 2016

zbMATH: 1341.62116
MathSciNet: MR3476614
Digital Object Identifier: 10.1214/15-AOS1382

Subjects:
Primary: 62H12 , 81P50
Secondary: 62C20 , 62P35 , 81P45 , 81P68

Keywords: compressed sensing , density matrix , minimax estimation , Pauli matrices , quantum measurement , Quantum probability , quantum statistics , sparse representation , spectral norm

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.44 • No. 2 • April 2016
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