Statistics Papers

Document Type

Journal Article

Date of this Version

2016

Publication Source

The Annals of Statistics

Volume

44

Issue

2

Start Page

682

Last Page

712

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.

Copyright/Permission Statement

The original and published work is available at: https://projecteuclid.org/euclid.aos/1458245732#abstract

Keywords

Compressed sensing, density matrix, Pauli matrices, quantum measurement, quantum probability, quantum statistics, sparse representation, spectral norm, minimax estimation

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Date Posted: 27 November 2017

This document has been peer reviewed.