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Generation and Coherent Control of Pulsed Quantum Frequency Combs
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Optimal Sparse Eigenspace and Low-Rank Density Matrix Estimation for Quantum Systems.

Tony Cai1, Donggyu Kim2, Xinyu Song3

  • 1Department of Statistics, the Wharton School, University of Pennsylvania.

Journal of Statistical Planning and Inference
|December 28, 2020
PubMed
Summary
This summary is machine-generated.

This study introduces new methods for estimating quantum states using Pauli measurements. The iterative thresholding sparse principal component analysis (ITSPCA) method is shown to be optimal for reconstructing large, low-rank quantum density matrices.

Keywords:
Iterative thresholdingPauli matrixminimax estimationprincipal component analysisquantum state tomography

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Area of Science:

  • Quantum Information Science
  • Quantum Computing
  • Quantum Technology

Background:

  • Quantum state tomography is crucial for estimating quantum states represented by density matrices.
  • Accurate state estimation is vital for advancing quantum science and technology.

Purpose of the Study:

  • To investigate eigenspace estimation and low-rank density matrix reconstruction using Pauli measurements.
  • To analyze the performance of principal component analysis (PCA) and iterative thresholding sparse PCA (ITSPCA) estimators.

Main Methods:

  • Studied ordinary principal component analysis (PCA) and iterative thresholding sparse PCA (ITSPCA) for eigenspace estimation.
  • Established convergence rates for both PCA and ITSPCA estimators.
  • Developed a method for reconstructing large low-rank density matrices using ITSPCA.

Main Results:

  • Established convergence rates for ordinary PCA and ITSPCA eigenspace estimators.
  • Demonstrated that the ITSPCA estimator achieves a rate-optimal performance.
  • Obtained the optimal convergence rate for reconstructing large low-rank density matrices via ITSPCA.

Conclusions:

  • The ITSPCA method offers a rate-optimal approach for quantum state tomography.
  • This work provides efficient methods for analyzing large quantum systems.
  • Numerical studies validate the finite sample performance of the proposed estimators.