Reliable confidence regions for quantum tomography using distribution moments

TL;DR

This paper introduces a computationally efficient method to determine reliable confidence regions for quantum tomography by approximating the distribution of the Hilbert-Schmidt distance through its moments, applicable to states and processes.

Contribution

It presents a novel scheme for estimating error bars in quantum tomography by calculating distribution moments, enhancing reliability and efficiency over existing methods.

Findings

Accurately approximates confidence intervals for quantum state estimates.

Validates the approach with simulations and quantum processor experiments.

Enables reliable quantum system characterization.

Abstract

Quantum tomography is a widely applicable method for reconstructing unknown quantum states and processes. However, its applications in quantum technologies usually also require estimating the difference between prepared and target quantum states with reliable confidence intervals. In this work we suggest a computationally efficient and reliable scheme for determining well-justified error bars for quantum tomography. We approximate the probability distribution of the Hilbert-Schmidt distance between the target state and the estimation, which is given by the linear inversion, by calculating its two moments. We also present a generalization of this approach for quantum process tomography and deriving confidence intervals for affine functions. We benchmark our approach for a number of quantum tomography protocols using both simulation and demonstration with the use of a cloud-accessible quantum processor. The obtained results pave the way for the use of the suggested scheme for the complete characterization of quantum systems of various natures.