Theory of versatile fidelity estimation with confidence

TL;DR

This paper introduces a versatile fidelity estimation method in quantum information that allows for flexible measurement choices while providing near-optimal confidence intervals, robustness, and practical accuracy.

Contribution

It develops a measurement-agnostic fidelity estimator with minimax optimal confidence intervals, outperforming existing methods in robustness and efficiency.

Findings

The method achieves near-minimax optimal confidence intervals.

It demonstrates robustness against experimental imperfections.

It provides accurate estimates with competitive sample complexity.

Abstract

Estimating the fidelity with a target state is important in quantum information tasks. Many fidelity estimation techniques present a suitable measurement scheme to perform the estimation. In contrast, we present techniques that allow the experimentalist to choose a convenient measurement setting. Our primary focus lies on a method that constructs an estimator with nearly minimax optimal confidence intervals for any specified measurement setting. We demonstrate, through a combination of theoretical and numerical results, various desirable properties of the method: robustness against experimental imperfections, competitive sample complexity, and accurate estimates in practice. We compare this method with Maximum Likelihood Estimation and the associated Profile Likelihood method, a Semi-Definite Programming based approach, direct fidelity estimation, quantum state verification, and classical shadows. Our method can also be used for estimating the expectation value of any observable with the same guarantees.