Monogamy of Nonlocal Games

Abstract

Bell monogamy relations characterize the trade-offs in Bell inequality violations among pairs of players in multiplayer settings. In this work, we introduce a method for extending monogamy relations from a distinguished set of configurations to monogamy relations on all possible multiplayer settings. Applying this approach, we show that nonlocality in the CHSH game arises in only two cases: the original two-player scenario and the four-player scenario on a line. While the bound for this four-player scenario follows from known quadratic monogamy constraints, we also establish two new six-party numerical monogamy relations that cannot be derived from existing results. In particular, we show there are points in the intersection of consecutive quadratic Bell monogamy relations which are not quantum realizable. Finally, we present a nonlocal game in which a single player can simultaneously saturate the quantum value with two other parties. This is the first known example of a nonlocal game unaffected by the monogamous nature of quantum entanglement.

References in corpus (22)

• Separability Criterion for Density Matrices
• Separability of Mixed States: Necessary and Sufficient Conditions
• Bell nonlocality
• Distributed Entanglement
• General Monogamy Inequality for Bipartite Qubit Entanglement
• A convergent hierarchy of semidefinite programs characterizing the set of quantum correlations
• Monogamy of entanglement and other correlations
• Bounding the set of quantum correlations
• Bell's theorem for general N-qubit states
• Monogamy of nonlocal quantum correlations
• Are general quantum correlations monogamous?
• Security proof for cryptographic protocols based only on the monogamy of Bell's inequality violations
• Strong monogamy conjecture for multiqubit entanglement: The four-qubit case
• Should Entanglement Measures be Monogamous or Faithful?
• Monogamy of Bell's inequality violations in non-signaling theories
• Correlation complementarity yields Bell monogamy relations
• Semidefinite programming relaxations for quantum correlations
• A synchronous game for binary constraint systems
• Elemental and tight monogamy relations in nonsignalling theories
• Strong monogamies of no-signaling violations for bipartite correlation Bell inequalities
• Bell monogamy relations in arbitrary qubit networks
• Extending the Known Region of Nonlocal Boxes that Collapse Communication Complexity

Cited by in corpus (3)

• Nonlocality of Quantum States can be Transitive
• The Richness of Bell Nonlocality: Generalized Bell Polygamy and Hyper-Polygamy
• Security of device-independent quantum key distribution via monogamy relations from multipartite information causality