Observers of quantum systems cannot agree to disagree

TL;DR

This paper extends the classical Agreement Theorem to quantum and no-signaling contexts, showing that quantum observers cannot agree to disagree, unlike in some postquantum theories, thus suggesting agreement as a potential physical principle.

Contribution

It generalizes Aumann's Agreement Theorem to quantum systems and constructs examples of postquantum no-signaling boxes where observers can agree to disagree.

Findings

Quantum observers cannot agree to disagree.

Postquantum no-signaling boxes can exhibit agreement to disagree.

Agreement may serve as a physical principle in quantum foundations.

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.