Full network nonlocality

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.

5+6 pages, 2+2 figures. RevTeX 4.1. The computational appendix is available at https://www.github.com/apozas/fullnn V2: Updated to match published version

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• Towards a minimal example of quantum nonlocality without inputs
• Sharing nonlocality in quantum network by unbounded sequential observers
• Persistency of non-n-local correlations in noisy linear networks
• Sharing Quantum Nonlocality in Star Network Scenarios
• Inflation: a Python library for classical and quantum causal compatibility
• Regarding the Maximal Qubit Violations of n-Locality in Star and Chain Networks
• The inflation hierarchy and the polarization hierarchy are complete for the quantum bilocal scenario
• Witnessing Non-Classicality in a Simple Causal Structure with Three Observable Variables
• Generalized $n$-locality inequalities in linear-chain network for arbitrary inputs scenario and their quantum violations
• Characterizing arbitrary quantum networks in the noisy intermediate-scale quantum era
• Multipartite Nonlocality in Clifford Networks
• Multi-system measurements in generalized probabilistic theories and their role in information processing
• Genuine network quantum nonlocality and self-testing