Density matrix estimation in quantum homodyne tomography
Yazhen Wang, Chenliang Xu · Statistica Sinica · 2014
Modern scientiflc studies often involve complex quantum systems, and scientists need to learn the systems from experiment data. As density matrices are usually employed to characterize the quantum states of the systems, this paper investigates estimation of density matrices for the quantum systems. We propose statistical methodologies to construct density matrix estimators and establish an asymptotic theory for the estimation methods. We show that the proposed density matrix estimators are consistent and have high convergence rates. A numerical study is conducted to demonstrate the good flnite sample performances of the proposed estimators.