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  • Letter
  • Open Access

Monogamy of nonlocal games

David Cui1,*, Arthur Mehta2, and Denis Rochette2

  • *Contact author: dzcui@mit.edu
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Phys. Rev. Research 7, L032003 – Published 7 July, 2025

DOI: https://doi.org/10.1103/1m7q-rgrh

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 in all possible multiplayer settings. Applying this approach, we show that nonlocality in the Clauser, Horne, Shimony, and Holt 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 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 an example of a nonlocal game unaffected by the monogamous nature of quantum entanglement.

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Phys. Rev. Research 7, L032003– Published 7 July, 2025
  • Received 7 June 2024
  • Accepted 21 May 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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