Optimal sparse eigenspace and low-rank density matrix estimation for quantum systems

DOI10.1016/j.jspi.2020.11.002zbMath1465.62182OpenAlexW3100629840WikidataQ104577578 ScholiaQ104577578MaRDI QIDQ830705

N. E. Zubov

Publication date: 7 May 2021

Published in: Journal of Statistical Planning and Inference (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jspi.2020.11.002

zbMATH Keywords

principal component analysisminimax estimationquantum state tomographyiterative thresholdingPauli matrix

Mathematics Subject Classification ID

Factor analysis and principal components; correspondence analysis (62H25) Estimation in multivariate analysis (62H12) Minimax procedures in statistical decision theory (62C20) Applications of statistics to physics (62P35) Quantum state estimation, approximate cloning (81P50)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quantum computation and quantum information
• Optimal large-scale quantum state tomography with Pauli measurements
• Sparse PCA-based on high-dimensional Itô processes with measurement errors
• Asymptotic theory for large volatility matrix estimation based on high-frequency financial data
• Sparse principal component analysis and iterative thresholding
• Minimax bounds for sparse PCA with noisy high-dimensional data
• Optimal sparse volatility matrix estimation for high-dimensional Itô processes with measurement errors
• Quantum Monte Carlo simulation
• User-friendly tail bounds for sums of random matrices
• Covariance regularization by thresholding
• Hypothesis tests for large density matrices of quantum systems based on Pauli measurements
• Adaptive thresholding for large volatility matrix estimation based on high-frequency financial data
• Quantum science and quantum technology
• Optimal estimation and rank detection for sparse spiked covariance matrices
• Vast volatility matrix estimation for high-frequency financial data
• Asymptotic equivalence of quantum state tomography and noisy matrix completion
• Minimax sparse principal subspace estimation in high dimensions
• Sparse PCA: optimal rates and adaptive estimation
• Quantum Computation and Quantum Information
• Adaptive Thresholding for Sparse Covariance Matrix Estimation
• Relative Perturbation Theory: I. Eigenvalue and Singular Value Variations
• Relative Perturbation Theory: II. Eigenspace and Singular Subspace Variations
• On Consistency and Sparsity for Principal Components Analysis in High Dimensions
• FAST CONVERGENCE RATES IN ESTIMATING LARGE VOLATILITY MATRICES USING HIGH-FREQUENCY FINANCIAL DATA

This page was built for publication: Optimal sparse eigenspace and low-rank density matrix estimation for quantum systems