Generalising Aumann's Agreement Theorem

• URL: http://arxiv.org/abs/2202.02156v2
• Date: Thu, 10 Feb 2022 11:43:24 GMT
• Title: Generalising Aumann's Agreement Theorem
• Abstract summary: Aumann's celebrated theorem says that a group of agents who once shared a common prior probability distribution cannot assign different posteriors to a given proposition. We argue that agreeing to disagree is impossible in quantum theory.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Aumann's celebrated theorem says that a group of agents who once shared a common prior probability distribution cannot assign different posteriors to a given proposition, should these agents have common knowledge about their posteriors. In other words, rational agents cannot agree to disagree. Aumann's agreement theorem was one of the first attempts to formalise and explore the role played by common knowledge in decision theory. Recently, we have seen a resurfacing of the debate around possible (quantum) extensions of Aumann's results. This paper contributes to this discussion. First, as expected, we argue that agreeing to disagree is impossible in quantum theory. Secondly, and based on the quantum argument, we show that agreeing to disagree is also forbidden in any generalised probability theory.

Related papers

• Aumann's theorem beyond ontology: quantum, postquantum, and indefinite causal order [0.0]
  We derive an operational version of Aumann's agreement theorem without assuming an objective state of the world.<n>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.<n>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.
  arXiv  Detail & Related papers  (2026-03-24T18:00:00Z)
• The Quantum Agreement Theorem [0.0]
  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.
  arXiv  Detail & Related papers  (2025-11-26T10:40:11Z)
• Another quantum version of Sanov theorem [53.64687146666141]
  We study how to extend Sanov theorem to the quantum setting. We propose another quantum version of Sanov theorem by considering the quantum analog of the empirical distribution.
  arXiv  Detail & Related papers  (2024-07-26T07:46:30Z)
• What Does '(Non)-Absoluteness of Observed Events' Mean? [0.0]
  We argue that the Wigner's friend paradox, the theorem of Bong et al and the theorem of Lawrence et al are all best understood as demonstrating that if quantum mechanics is universal. We also argue that these theorems taken together suggest interesting possibilities for a different kind of relational approach in which dynamical states are relativized whilst observed events are absolute.
  arXiv  Detail & Related papers  (2023-09-06T17:13:31Z)
• Connecting classical finite exchangeability to quantum theory [69.62715388742298]
  Exchangeability is a fundamental concept in probability theory and statistics. We show how a de Finetti-like representation theorem for finitely exchangeable sequences requires a mathematical representation which is formally equivalent to quantum theory.
  arXiv  Detail & Related papers  (2023-06-06T17:15:19Z)
• On the Categoricity of Quantum Mechanics [0.0]
  The paper offers an argument against an intuitive reading of the Stone-von Neumann theorem as a categoricity result. It argues that, against what is usually taken to be the case, this theorem does not entail any model-theoretical difference between the theories that validate it and those that don't.
  arXiv  Detail & Related papers  (2023-04-20T06:19:13Z)
• Comment on 'The operational foundations of PT-symmetric and quasi-Hermitian quantum theory' [0.0]
  We point out that the author's main discovery (viz., that the QHQT does not extend the standard quantum theory) is not new. A few other, mathematically consistent GPT-like theories are already available in the literature.
  arXiv  Detail & Related papers  (2023-01-03T17:06:31Z)
• No-local-broadcasting theorem for non-signalling behaviours and assemblages [0.0]
  The no-broadcasting theorem is a fundamental result in quantum information theory.<n>We prove Joshi, Grudka, and Horodecki$otimes 4$ conjectured that one cannot locally broadcast nonlocal behaviours.
  arXiv  Detail & Related papers  (2022-11-25T19:08:28Z)
• Incompatibility of observables, channels and instruments in information theories [68.8204255655161]
  We study the notion of compatibility for tests of an operational probabilistic theory. We show that a theory admits of incompatible tests if and only if some information cannot be extracted without disturbance.
  arXiv  Detail & Related papers  (2022-04-17T08:44:29Z)
• Observers of quantum systems cannot agree to disagree [55.41644538483948]
  We ask whether agreement between observers can serve as a physical principle that must hold for any theory of the world. We construct examples of (postquantum) no-signaling boxes where observers can agree to disagree.
  arXiv  Detail & Related papers  (2021-02-17T19:00:04Z)
• Impossibility of creating a superposition of unknown quantum states [16.467540842571328]
  We show that the existence of a protocol that superposes two unknown pure states with nonzero probability leads to violation of other no-go theorems. Such a protocol can be used to perform certain state discrimination and cloning tasks that are forbidden in quantum theory.
  arXiv  Detail & Related papers  (2020-11-04T13:25:42Z)
• From a quantum theory to a classical one [117.44028458220427]
  We present and discuss a formal approach for describing the quantum to classical crossover. The method was originally introduced by L. Yaffe in 1982 for tackling large-$N$ quantum field theories.
  arXiv  Detail & Related papers  (2020-04-01T09:16:38Z)
• Escape from the Quantum Pigeon Conundrum [52.77024349608834]
  The Pigeon Counting Principle (PCP) states that if one distributes three pigeons among two boxes there must be at least two pigeons in one of the boxes. Here we prove via a set of operator identities that the PCP is not violated within quantum mechanics, regardless of interpretation.
  arXiv  Detail & Related papers  (2020-02-05T17:30:19Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.