Robust self-testing and certified randomness based on chained Bell inequality

TL;DR

This paper presents a robust, device-independent self-testing method based on chained Bell inequalities, utilizing a sum-of-squares technique to optimize quantum violations and certify randomness even with noise.

Contribution

It introduces a systematic SOS-based approach for dimension-independent optimization of chained Bell inequalities, enabling robust self-testing and certified randomness generation.

Findings

Developed a sum-of-squares technique for optimized quantum violation derivation.

Achieved robust self-testing in noisy experimental conditions.

Demonstrated two-bit device-independent randomness generation with robustness analysis.

Abstract

Self-testing is the strongest certification procedure that uniquely characterizes the physical system based on the observed statistics, without any knowledge of the inner workings of the devices. The optimal quantum violation of a Bell inequality enables such a device-independent (DI) self-testing of the source and the measurement devices. In this work, we demonstrate the DI self-testing based on the arbitrary-input chained Bell inequality. We devise a systematic and elegant sum-of-squares (SOS) technique enabling dimension-independent optimization of the quantum violation. Our approach enables the derivation of the state along with the relationship between the local observables directly from the optimization condition. One significant aspect is the robustness of such self-testing in real experimental situations involving noise and imperfection, leading to deviation from the optimal quantum violation. We provide an analytical technique for robust self-testing in the presence of noise. As an application of our scheme, we demonstrate the generation of two bit DI randomness and analyze the robustness of such randomness. Our optimization method is both simple and elegant, making it suitable for deriving the optimal quantum violation of various arbitrary-input Bell inequalities.