  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.
