Bell monogamy relations in arbitrary qubit networks

Abstract

Characterizing trade-offs between simultaneous violations of multiple Bell inequalities in a large network of qubits is computationally demanding. We propose a graph-theoretic approach to efficiently produce Bell monogamy relations in arbitrary arrangements of qubits. All the relations obtained for bipartite Bell inequalities are tight and leverage only a single Bell monogamy relation. This feature is unique to bipartite Bell inequalities, as we show that there is no finite set of such elementary monogamy relations for multipartite inequalities. Nevertheless, many tight monogamy relations for multipartite inequalities can be obtained with our method as shown in explicit examples.

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• Unmasking the Polygamous Nature of Quantum Nonlocality
• Note on Product-Form Monogamy Relations for Nonlocality and Other Correlation Measures
• Monogamy of Nonlocal Games
• Genuine monogamy relations in no-signaling theories - a geometric approach
• The Richness of Bell Nonlocality: Generalized Bell Polygamy and Hyper-Polygamy
• Quantum Monogamy with Predetermined Events