Bell monogamy relations in arbitrary qubit networks

TL;DR

This paper introduces a graph-theoretic method to efficiently derive tight Bell monogamy relations in arbitrary qubit networks, simplifying the analysis of quantum correlations and their trade-offs.

Contribution

It presents a novel approach that produces tight bipartite Bell monogamy relations efficiently and extends the method to multipartite inequalities with explicit examples.

Findings

All bipartite Bell relations obtained are tight.

The method leverages only a single Bell monogamy relation for bipartite cases.

Many tight multipartite monogamy relations can be derived using this approach.

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.