Optimal large-scale quantum state tomography with Pauli measurements
Tony Cai, Donggyu Kim, Yazhen Wang, Ming Yuan, Harrison H. Zhou
The Annals of Statistics · 2016 · Volume 44 · Issue 2
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.
Keywords
62C20, 62H12, 62P35, 81P45, 81P50, 81P68, compressed sensing, density matrix, minimax estimation, Pauli matrices, quantum measurement, Quantum probability, quantum statistics, sparse representation, spectral norm
Enable JavaScript for citation tools and additional paper interactions.