Robustness analysis in static and dynamic quantum state tomography

TL;DR

This paper analyzes how errors in measurement devices and system dynamics affect the accuracy of quantum state tomography, providing bounds on estimation errors and demonstrating their scaling through simulations.

Contribution

It introduces explicit bounds on the robustness of static and dynamic quantum state tomography under perturbations, using linear regression estimation methods.

Findings

Derived bounds on MSE due to device and Hamiltonian errors

Simulations show bounds scale with resources in qubit systems

Robustness analysis applicable to practical quantum experiments

Abstract

Quantum state tomography is a core task in quantum system identification. Real experimental conditions often deviate from nominal designs, introducing errors in both the measurement devices and the Hamiltonian governing the system's dynamics. In this paper, we investigate the robustness of quantum state tomography against such perturbations in both static and dynamic settings using linear regression estimation. We derive explicit bounds that quantify how bounded errors in the measurement devices and the Hamiltonian affect the mean squared error (MSE) upper bound in each scenario. Numerical simulations for qubit systems illustrate how these bounds scale with resources.