Disagreement with Wigner

Vinicius P. Rossi

In 1962, Eugene P. Wigner introduced a thought experiment that highlighted the incompatibility in quantum mechanics between unitary evolution and wave function reduction in a measurement. This work resulted in a class of thought experiments often called Wigner\'s Friend Scenarios, which have been providing insights over many frameworks and interpretations of quantum theory. Recently, a no-go theorem obtained by Daniela Frauchiger and Renato Renner brought attention back to the Wigner\'s Friend and its potential of putting theories to test. Many answers to this result pointed out how timing in the thought experiment could be yielding a paradox. In this work, we ask what would happen if the isolated friend in a Wigner\'s Friend Scenario did not share a time reference frame with the outer observer, and time should be tracked by a quantum clock. For this purpose, we recollect concepts provided by the theory of quantum reference frames and the quantum resource theory of asymmetry, to learn how to internalize time in this scenario, and introduce a model for a feasible quantum clock proposed by Mischa P. Woods, Ralph Silva and Jonathan Oppenheim, called the quasi-ideal clock. Our results have shown that no decoherent behavior comes from this approach, and the disagreement between the superobserver and its friend persists even for an imprecise clock, indicating that the source of paradox in a Wigner\'s Friend Scenario may be elsewhere.

L. E. Ballentine

Vinicius P. Rossi, Diogo O. Soares-Pinto

In 1962, Eugene P. Wigner [in Philosophical Reflections and Syntheses (Springer, Berlin, 1995), p. 247] introduced a thought experiment that highlighted the incompatibility in quantum theory between unitary evolution and wave function reduction in a measurement. This work resulted in a class of thought experiments often called Wigner's friend scenarios, which have been providing insights over many frameworks and interpretations of quantum theory. Recently, a no-go theorem obtained by D. Frauchiger and R. Renner [Nat. Commun. 9, 3711 (2018)] brought attention back to the Wigner's friend and its potential of putting theories to the test. Many answers to this result pointed out how timing in the thought experiment could be yielding a paradox. In this work, we ask what would happen if the isolated friend in a Wigner's friend scenario did not share a time reference frame with the outer observer, and time were tracked by a quantum clock. For this purpose, we recollect concepts provided by the theory of quantum reference frames and the quantum resource theory of asymmetry, to learn how to internalize time in this scenario, and introduce a model for a feasible quantum clock proposed by M. P. Woods, R. Silva, and J. Oppenheim [Ann. Henri Poincar\'e 20, 125 (2019)] called the quasi-ideal clock. Our results have shown that this approach produces no decoherent behavior, and the disagreement between the superobserver and its friend persists even for an imprecise clock on Wigner's side. However, the Gaussian spread of this clock model can control which observables do not raise a paradox, indicating the relevance of deepening this analysis.

Henry Pierce Stapp

Carlo Cepollaro, Andrea Di Biagio

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.

Wenbin Cai

The traditional quantization algorithms lead high original disagreement rate in the secret key extraction courses,which can reduce the final secret key rate.Aiming at this problem,a pretreatment method based on parity checking is proposed in this paper.The legitimate parities divide the quantization results into groups,and exchange the parity of the groups over a public channel.It removes the groups whose parities are disagreed to reduce the original disagreement rate.Simulation results demonstrate that the new pretreatment method can not only have excellent ability of reducing the original disagreement rate,especially in the case of high original disagreement rate.The remainder ratio of this pretreatment method is improved by nearly nine times when the original disagreement rate is 0.26.