Aumann's theorem beyond ontology: quantum, postquantum, and indefinite causal order

TL;DR

This paper extends Aumann's agreement theorem beyond classical ontology to quantum, postquantum, and indefinite causal order scenarios by deriving an operational version that relies solely on observations, not an objective state.

Contribution

It introduces an operational framework for Aumann's theorem applicable to quantum and postquantum phenomena, bypassing the need for an underlying objective state of the world.

Findings

The theorem holds in quantum theory and indefinite causal order scenarios.

It clarifies the conditions under which agreement theorems may fail, such as Wigner's friend situations.

The approach unifies classical and quantum agreement results without assuming an objective state.

Abstract

Agreement theorems are no-go results about rational disagreement: if two agents start from a common prior and their posterior beliefs are common knowledge, they cannot assign different probabilities to the same event. Standard treatments of the result have the agents reason about an underlying state of the world, which has lead some to ask whether the result can extend to quantum or postquantum phenomena, where such a description may no longer be appropriate. We derive an operational version of Aumann's agreement theorem without assuming an objective state of the world and instead focusing only on what is observed. This allows us to establish the theorem's validity in quantum theory and even in situations with indefinite causal order or involving hypothetical postquantum phenomena. We comment on seemingly contradictory results in the literature and point to the one place where the theorem might fail: Wigner's friend-type situations.