Genuine monogamy relations in no-signaling theories - a geometric approach

• URL: http://arxiv.org/abs/1812.01494v2
• Date: Tue, 07 Oct 2025 07:09:55 GMT
• Title: Genuine monogamy relations in no-signaling theories - a geometric approach
• Authors: Junghee Ryu, Daemin Lee, Jinhyoung Lee, Paweł Kurzyński, Dagomir Kaszlikowski,
• Abstract summary: We show that simple geometric properties of probabilistic spaces, in conjunction with no-signaling principle, lead to genuine monogamy relations.<n>We derive Svetlichny-Zohren-Gill type Bell inequalities for $d$-dimensional tripartite systems.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum correlations are subject to certain distribution rules represented by so-called monogamy relations. Derivation of monogamy relations for multipartite systems is a non-trivial problem, as the multipartite correlations reveal their behaviors in a way different from bipartite systems. We here show that simple geometric properties of probabilistic spaces, in conjunction with no-signaling principle, lead to genuine monogamy relations for a large class of Bell type inequalities for many qubits. The term of 'genuine' implies that only one out of $N$ Bell inequalities exhibits a quantum violation. We also generalize our method to qudits. Using the similar geometric approach with a quasi-distance employed, we derive Svetlichny-Zohren-Gill type Bell inequalities for $d$-dimensional tripartite systems, and show their monogamous nature.

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