Noise-Robust Self-Testing: Detecting Non-Locality in Noisy Non-Local Inputs

TL;DR

This paper introduces a systematic framework for comparing noise-robustness in quantum self-testing protocols, demonstrating that the CHSH game is most robust under equal resources and providing tools for practical quantum device certification.

Contribution

It proposes three measures of noise-robustness, identifies convincingness as the most nuanced, and compares the robustness of different non-local games systematically.

Findings

Convincingness is the most effective measure of noise-robustness.

CHSH game exhibits the highest noise-robustness among tested games with equal resources.

Some 2-CHSH variants outperform CHSH at high resource costs with unequal resources.

Abstract

Non-local games test for non-locality and entanglement in quantum systems and are used in self-tests for certifying quantum states in untrusted devices. However, these protocols are tailored to ideal states, so realistic noise prevents maximal violations and leaves many partially non-local states undetected. Selecting self-tests based on their 'robustness' to noise can tailor protocols to specific applications, but current literature lacks a standardized measure of noise-robustness. Creating such a measure is challenging as there is no operational measure for comparing tests of different dimensionalities and input-output settings. We propose and study three comparative measures: noise-tolerance, convincingness, and an analytic approximation of convincingness called the gapped score. Our computational experiments and analytic framework demonstrate that convincingness provides the most nuanced measure for noise-robustness. We then show that the CHSH game has the highest noise-robustness compared to more complex games (2-CHSH variants and the Magic Square Game) when given equal resources, while with unequal resources, some 2-CHSH variants can outperform CHSH at a high resource cost. This work provides the first systematic and operational framework for comparing noise-robustness in self-testing protocols, laying a foundation for theoretical advances in understanding noise-robustness of self-tests and practical improvements in quantum resource utilization.