Maximum-Likelihood Quantum State Tomography by Cover's Method with Non-Asymptotic Analysis

We propose an iterative algorithm that computes the maximum-likelihood estimate in quantum state tomography. The optimization error of the algorithm converges to zero at an O ( ( 1 / k ) log D ) rate, where k denotes the number of iterations and D denotes the dimension of the quantum state. The per-iteration computational complexity of the algorithm is O \(D ^ 3 + N D ²\), where N denotes the number of measurement outcomes. The algorithm can be considered as a parameter-free correction of the R ρR method \[A. I. Lvovsky. Iterative maximum-likelihood reconstruction in quantum homodyne tomography. J. Opt. B: Quantum Semiclass. Opt. 2004\] \[G. Molina-Terriza et al. Triggered qutrits for quantum communication protocols. Phys. Rev. Lett. 2004.\].