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
Recommended Citation
Cai, T., Kim, D., Wang, Y., Yuan, M., & Zhou, H. H. (2016). Optimal Large-Scale Quantum State Tomography With Pauli Measurements. The Annals of Statistics, 44 (2), 682-712. http://dx.doi.org/10.1214/15-AOS1382
Date Posted: 27 November 2017
This document has been peer reviewed.