Fast and simple quantum state estimation

TL;DR

This paper introduces a fast, robust iterative method for quantum state estimation that outperforms existing techniques in speed and accuracy, especially in high-dimensional systems and practical error conditions.

Contribution

The authors develop a novel iterative algorithm for quantum state estimation that converges rapidly and is robust to errors, with specific efficiency gains for certain measurement sets.

Findings

Converges in a single iteration for mutually unbiased bases.

Outperforms maximum likelihood estimation in runtime.

Achieves high fidelity in state reconstruction.

Abstract

We present an iterative method to solve the multipartite quantum state estimation problem. We demonstrate convergence for any informationally complete set of generalized quantum measurements in every finite dimension. Our method exhibits fast convergence in high dimension and strong robustness under the presence of realistic errors both in state preparation and measurement stages. In particular, for mutually unbiased bases and tensor product of generalized Pauli observables it converges in a single iteration. We show outperformance of our algorithm with respect to the state-of-the-art of maximum likelihood estimation methods both in runtime and fidelity of the reconstructed states.