Optimal large-scale quantum state tomography with Pauli measurements
研究了基于泡利测量估计高维密度矩阵的统计问题，在稀疏性假设下给出了谱范数和Frobenius范数损失下的极小化最优收敛速率，并证明阈值方法能达到该速率。
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.