Robust error bars for quantum tomography

TL;DR

This paper introduces a method for constructing reliable likelihood ratio confidence regions in quantum tomography, providing nearly optimal error bounds for estimating quantum states or processes from measurement data.

Contribution

It presents a novel procedure for assigning likelihood ratio confidence regions, enhancing the rigor and reliability of quantum state and process estimation.

Findings

LR regions are nearly optimally small

The method improves the reliability of quantum tomography estimates

Provides a rigorous framework for error analysis in quantum state estimation

Abstract

In quantum tomography, a quantum state or process is estimated from the results of measurements on many identically prepared systems. Tomography can never identify the state or process exactly. Any point estimate is necessarily "wrong" -- at best, it will be close to the true state. Making rigorous, reliable statements about the system requires region estimates. In this article, I present a procedure for assigning likelihood ratio (LR) confidence regions, an elegant and powerful generalization of error bars. In particular, LR regions are almost optimally powerful -- i.e., they are as small as possible.