Monogamy of Nonlocal Games

TL;DR

This paper develops a method to extend Bell monogamy relations to all multiplayer settings, revealing new constraints on nonlocality and presenting a game where a player can simultaneously maximize quantum correlations with multiple others.

Contribution

It introduces a novel approach for extending monogamy relations to all multiplayer configurations and presents new monogamy relations and a unique nonlocal game unaffected by monogamy.

Findings

Nonlocality in CHSH arises only in specific multiplayer scenarios.

New six-party monogamy relations are established.

A nonlocal game is constructed where one player saturates quantum value with two others.

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.