The Exclusivity Principle Determines the Correlation Monogamy

TL;DR

This paper shows that the exclusivity principle explains the monogamy of quantum correlations using graph theory, providing criteria and examples for various types of nonlocality experiments.

Contribution

It introduces a graph-theoretic criterion based on fractional packing and Lovász numbers to determine correlation monogamy, linking it to the exclusivity principle.

Findings

Monogamy can be derived from the exclusivity principle using graph theory.

Provides criteria involving fractional packing and Lovász numbers for monogamy.

Includes new monogamy relations for Svetlichny's genuine nonlocality.

Abstract

Adopting the graph-theoretic approach to the correlation experiments, we analyze the origin of monogamy and prove that it can be recognized as a consequence of the exclusivity principle(EP). We provide an operational criterion for monogamy: if the fractional packing number of the graph corresponding to the union of event sets of several physical experiments does not exceed the sum of independence numbers of each individual experiment graph, then these experiments are monogamous. As applications of this observation, several examples are provided, including the monogamy for experiments of Clauser-Horne-Shimony-Holt (CHSH) type, Klyachko-Can-Binicio\u{g}lu-Shumovsky (KCBS) type, and for the first time, we give some monogamy relations of Svetlichny's genuine nonlocality. We also give the necessary and sufficient conditions for several experiments to be monogamous: several experiments are monogamous if and only if the Lov\'asz number of the union exclusive graph is less than or equal to the sum of independence numbers of each exclusive graph.