The Quantum Agreement Theorem

• URL: http://arxiv.org/abs/2511.21258v1
• Date: Wed, 26 Nov 2025 10:40:11 GMT
• Title: The Quantum Agreement Theorem
• Authors: María García Díaz, Adam Brandenburger, Giannicola Scarpa,
• Abstract summary: We define the modality of "common certainty" through a hierarchy of certainty operators acting on each agent's Hilbert space.<n>In commuting cases, common certainty leads to equality of the agents' conditional probabilities, recovering a QM analog of the classical theorem.<n>We 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.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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. Agreement is restored once measurement outcomes are recorded in a classical register. The classical Agreement Theorem can therefore be seen as emergent from the quantum world via recording. We 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.

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