Confidence Polytopes in Quantum State Tomography

TL;DR

This paper introduces a simple, efficient method for constructing confidence polytopes in quantum state tomography, providing reliable error estimates with high probability, demonstrated through practical experimental examples.

Contribution

It presents a novel scheme for generating confidence regions in quantum state tomography using quantum Clopper-Pearson intervals, which are computationally efficient and reliable.

Findings

Confidence polytopes can be computed efficiently.

The scheme provides high-probability error bounds.

Practical usability demonstrated in experiments.

Abstract

Quantum State Tomography is the task of inferring the state of a quantum system from measurement data. A reliable tomography scheme should not only report an estimate for that state, but also well-justified error bars. These may be specified in terms of confidence regions, i.e., subsets of the state space which contain the system's state with high probability. Here, building upon a quantum generalisation of Clopper-Pearson confidence intervals--a notion known from classical statistics--we present a simple and reliable scheme for generating confidence regions. These have the shape of a polytope and can be computed efficiently. We provide several examples to demonstrate the practical usability of the scheme in experiments.