Optimal large-scale quantum state tomography with Pauli measurements

TL;DR

This paper develops optimal methods for estimating high-dimensional quantum states using Pauli measurements, establishing minimax rates and demonstrating effective thresholding techniques with numerical validation.

Contribution

It provides the first minimax optimal rates for quantum state estimation under sparsity assumptions with Pauli measurements and introduces a practical thresholding estimator.

Findings

Achieves minimax optimal convergence rates under spectral and Frobenius norms.

Proposes a thresholding estimator that attains these optimal rates.

Numerical experiments confirm the estimator's effectiveness.

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.