Robust Self-Testing of Multiqudit Supersinglet Slater States via Constant Number of Binary Measurements

Abstract

Self-testing is a powerful device-independent technique that enables one to deduce the forms of both the quantum state and the measurements involved in a physical experiment based solely on observed correlations. Although numerous schemes for self-testing multipartite entangled states have been proposed, they are typically difficult to implement experimentally, as their complexity increases significantly with the number of subsystems or the local dimension. In this work, we introduce the first self-testing scheme of a relevant class of multiqudit genuinely entangled states that exploits only a constant number of binary measurements per observer, which significantly reduces the experimental effort to implement the scheme. Specifically, it enables the self-testing of multipartite Slater (or supersinglet) states composed of $d$ qu\textit{d}its with odd $d$ using only four two-outcome measurements per observer. Moreover, we prove that our scheme is robust to noise and experimental imperfections. For systems of even local dimension $d$, we also provide an adapted version of the scheme that requires only $d$ binary measurements per observer.