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Observers of quantum systems cannot agree to disagree

Author

Listed:
  • Patricia Contreras-Tejada

    (Instituto de Ciencias Matemáticas)

  • Giannicola Scarpa

    (Universidad Politécnica de Madrid)

  • Aleksander M. Kubicki

    (Universidad Complutense de Madrid)

  • Adam Brandenburger

    (Tandon School of Engineering, NYU Shanghai, New York University)

  • Pierfrancesco La Mura

    (HHL Leipzig Graduate School of Management)

Abstract

Is the world quantum? An active research line in quantum foundations is devoted to exploring what constraints can rule out the postquantum theories that are consistent with experimentally observed results. We explore this question in the context of epistemics, and ask whether agreement between observers can serve as a physical principle that must hold for any theory of the world. Aumann’s seminal Agreement Theorem states that two observers (of classical systems) cannot agree to disagree. We propose an extension of this theorem to no-signaling settings. In particular, we establish an Agreement Theorem for observers of quantum systems, while we construct examples of (postquantum) no-signaling boxes where observers can agree to disagree. The PR box is an extremal instance of this phenomenon. These results make it plausible that agreement between observers might be a physical principle, while they also establish links between the fields of epistemics and quantum information that seem worthy of further exploration.

Suggested Citation

  • Patricia Contreras-Tejada & Giannicola Scarpa & Aleksander M. Kubicki & Adam Brandenburger & Pierfrancesco La Mura, 2021. "Observers of quantum systems cannot agree to disagree," Nature Communications, Nature, vol. 12(1), pages 1-7, December.
    • Handle: RePEc:nat:natcom:v:12:y:2021:i:1:d:10.1038_s41467-021-27134-6
    DOI: 10.1038/s41467-021-27134-6
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    References listed on IDEAS

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    1. Robert Aumann & Adam Brandenburger, 2014. "Epistemic Conditions for Nash Equilibrium," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 5, pages 113-136, World Scientific Publishing Co. Pte. Ltd..
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    5. Parikh, Rohit & Krasucki, Paul, 1990. "Communication, consensus, and knowledge," Journal of Economic Theory, Elsevier, vol. 52(1), pages 178-189, October.
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    7. Khrennikov, Andrei, 2015. "Quantum version of Aumann’s approach to common knowledge: Sufficient conditions of impossibility to agree on disagree," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 89-104.
    8. Miguel Navascués & Yelena Guryanova & Matty J. Hoban & Antonio Acín, 2015. "Almost quantum correlations," Nature Communications, Nature, vol. 6(1), pages 1-7, May.
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    Cited by:

    1. Christian W. Bach & Jérémie Cabessa, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Post-Print hal-04271274, HAL.
    2. Bach, Christian W. & Cabessa, Jérémie, 2023. "Lexicographic agreeing to disagree and perfect equilibrium," Journal of Mathematical Economics, Elsevier, vol. 109(C).

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