Constructing multipartite Bell inequalities from stabilizers

Abstract

Bell inequality with a self-Testing property has played an important role in quantum information processing with both fundamental and practical significance. However, it is generally challenging to find Bell inequalities used for self-Testing multipartite states, and actually, there are not many known candidates. In this work we propose a systematic framework to construct Bell inequalities from stabilizers which are maximally violated by general stabilizer states, with two observables for each local party. We show that the constructed Bell inequalities can self-Test any stabilizer state if and only if these stabilizers can uniquely determine the state in a device-dependent manner. This bridges the gap between device-independent and device-dependent verification methods. Our framework can provide plenty of Bell inequalities for self-Testing N-party stabilizer states. Among them, we give two families of Bell inequalities with different advantages: (1) a family of Bell inequalities with a constant ratio of quantum and classical bounds using 2N correlations, and (2) single pair inequalities improving on all previous robustness self-Testing bounds using N+1 correlations, which are both efficient and robust for realizations in multipartite systems.