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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.21258 |
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Table of Contents:
- We formulate and prove an Agreement Theorem for quantum mechanics (QM), describing when two agents, represented by separate laboratories, can or cannot maintain differing probability estimates of a shared quantum property of interest. Building on the classical framework (Aumann, 1976), we define the modality of ``common certainty" through a hierarchy of certainty operators acting on each agent's Hilbert space. In the commuting case -- when all measurements and event projectors commute -- common certainty leads to equality of the agents' conditional probabilities, recovering a QM analog of the classical theorem. By contrast, when non-commuting operators are allowed, the certainty recursion can stabilize with different probabilities. This yields common certainty of disagreement (CCD) as a distinctive QM phenomenon. We show that agreement will nevertheless re-emerge if measurement outcomes are recorded in a classical register. We also establish an impossibility result stating that QM forbids a scenario where one agent is certain that a property of interest occurs, and is also certain that the other agent is certain that the property does not occur. In this sense, QM admits non-classical disagreement, but disagreement is still bounded in a disciplined way. We argue that our analysis offers a rigorous approach to the longstanding issue of how to understand intersubjectivity across agents in QM.