Full network nonlocality

TL;DR

This paper introduces the concept of full network nonlocality, a stronger form of nonlocal correlations requiring all network links to share nonlocal resources, and provides methods to detect it in quantum networks.

Contribution

It defines full network nonlocality, proves its distinction from standard nonlocality, and develops systematic methods and witnesses for detecting it in various quantum network scenarios.

Findings

Star network Bell test can detect full network nonlocality.

Polynomial witnesses for full network nonlocality are constructed.

Quantum Elegant Joint Measurements can violate these witnesses.

Abstract

Networks have advanced the study of nonlocality beyond Bell's theorem. Here, we introduce the concept of full network nonlocality, which describes correlations that necessitate all links in a network to distribute nonlocal resources. Showcasing that this notion is stronger than standard network nonlocality, we prove that the most well-known network Bell test does not witness full network nonlocality. In contrast, we demonstrate that its generalisation to star networks is capable of detecting full network nonlocality in quantum theory. More generally, we point out that established methods for analysing local and theory-independent correlations in networks can be combined in order to systematically deduce sufficient conditions for full network nonlocality in any network and input/output scenario. We demonstrate the usefulness of these methods by constructing polynomial witnesses of full network nonlocality for the bilocal scenario. Then, we show that these inequalities can be violated via quantum Elegant Joint Measurements.