Bell nonlocality in networks

Abstract

Bell’s theorem proves that quantum theory is inconsistent with local physical models. It has propelled research in the foundations of quantum theory and quantum information science. As a fundamental feature of quantum theory, it impacts predictions far beyond the traditional scenario of the Einstein-Podolsky-Rosen paradox. In the last decade, the investigation of nonlocality has moved beyond Bell’s theorem to consider more sophisticated experiments that involve several independent sources that distribute shares of physical systems among many parties in a network. Network scenarios, and the nonlocal correlations that they give rise to, lead to phenomena that have no counterpart in traditional Bell experiments, thus presenting a formidable conceptual and practical challenge. This review discusses the main concepts, methods, results and future challenges in the emerging topic of Bell nonlocality in networks.

Full Network Nonlocality

“…We have also conducted a numerical search for a simultaneous quantum violation of the inequalities ( 6) and ( 7) and found no improvement on the presented protocol. Even though the critical visibility here is slightly larger than that required for violating (5), it is important to note that this scenario is considerably simpler: it requires fewer copies, fewer parties, and a simpler joint measurement. Also, it highlights the relevance of more general entangled measurements in network nonlocality.…”

“…In the last decade, much research in quantum information has been dedicated to understanding correlations in networks (see Ref. [5] for a review).…”

Proofs of network quantum nonlocality aided by machine learning

“…This phenomenon, known as quantum nonlocality, is now the basis of many protocols that process information encoded in quantum systems [2][3][4]. In the last decade, both theoretical advances and experimental improvements have allowed to shift the focus to multipartite scenarios, called networks, where many independent sources distribute physical systems among different, overlapping collections of parties [5,6]. The study of nonlocality in these network scenarios is generating a very exciting research field.…”

Outer approximations of classical multi-network correlations

“…Beyond the setting of Bell's theorem, there are a number of reasons to be interested in causal compatibility in greater generality [TPKLR21]. Here, we are concerned with causal structures called networks that feature a number of independent, unobserved parameters, which we refer to as "sources", that may influence a number of observed parameters, which we refer to as the outcomes of "agents": this naming convention reflects the quantum information mindset where the observed parameters would be the outcomes of measurements that human agents would carry out in a lab.…”

“…In order to obtain guarantees that a fair amount of the search space has been sampled, it is crucial to have access to tractable outer approximations of the set of outcome distributions. A useful review for that purpose is that of [TPKLR21]. One basic analytical tool is Finner's inequality [RWB + 19], that provides simple bounds on achievable correlations in non-signaling networks.…”