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

arXiv: https://arxiv.org/abs/2110.00747 · HTML: https://mlsanity.com/paper/2110.00747/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Oct 2021.

## Built on by (most cited first, 1 of 1)

- [Fast Minimization of Expected Logarithmic Loss via Stochastic Dual Averaging](https://mlsanity.com/paper/2311.02557/) (2023)

## Abstract (arXiv)

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 ρ R method [A. I. Lvovsky. Iterative maximum-likelihood reconstruction in quantum homodyne tomography. textitJ. Opt. B: Quantum Semiclass. Opt. 2004] [G. Molina-Terriza et al. Triggered qutrits for quantum communication protocols. textitPhys. Rev. Lett. 2004.].