Global convergence of diluted iterations in maximum-likelihood quantum tomography

TL;DR

This paper introduces a globally convergent algorithm for quantum state tomography that improves the diluted R ho R method by using an inexact stepsize, enabling practical and reliable maximum likelihood estimation.

Contribution

It provides a new interpretation and a globally convergent version of the diluted R ho R algorithm for quantum state tomography.

Findings

Proved global convergence under weaker assumptions.

Developed a practical algorithm suitable for implementation.

Enhanced reliability of maximum likelihood quantum state estimation.

Abstract

In this paper we present an inexact stepsize selection for the Diluted R\rho R algorithm, used to obtain the maximum likelihood estimate to the density matrix in quantum state tomography. We give a new interpretation for the diluted R\rho R iterations that allows us to prove the global convergence under weaker assumptions. Thus, we propose a new algorithm which is globally convergent and suitable for practical implementation.