Multi-agent paradoxes beyond quantum theory

Abstract

Which theories lead to a contradiction between simple reasoning principles and modelling observers' memories as physical systems? Frauchiger and Renner have shown that this is the case for quantum theory (Frauchiger and Renner 2018 Nat. Commun. 9 3711). Here we generalize the conditions of the Frauchiger-Renner result so that they can be applied to arbitrary physical theories, and in particular to those expressed as generalized probabilistic theories (GPTs) (Hardy 2001 arXiv:quant-ph/0101012; Barrett 2007 Phys. Rev. A 75 032304). We then apply them to a particular GPT, box world, and find a deterministic contradiction in the case where agents may share a PR box (Popescu and Rohrlich 1994 Found. Phys. 24 379-85), which is stronger than the quantum paradox, in that it does not rely on postselection. Obtaining an inconsistency for the framework of GPTs broadens the landscape of theories which are affected by the application of classical rules of reasoning to physical agents. In addition, we model how observers' memories may evolve in box world, in a way consistent with Barrett's criteria for allowed operations (Barrett 2007 Phys. Rev. A 75 032304; Gross et al 2010 Phys. Rev. Lett. 104 080402).Ordinary readers, forgive my paradoxes: one must make them when one reflects; and whatever you may say, I prefer being a man with paradoxes than a man with prejudices.

Testing quantum theory with thought experiments

“…One may also ask whether the conclusions obtained from the thought experiments presented here are specific to quantum theory, or whether they hold more generally. In [79], it was shown that, within the framework of generalised probability theories [80][81][82], which generalise the operational aspect of quantum theory, this is indeed the case for an experiment analogous to the FR thought experiment. Conversely, one may also apply classical multi-agent modal logic [83] to investigate Wigner's friend type experiments.…”

Automated Proof Search System for Logic of Correlated Knowledge

“…One of the latest development in this way is quantum modal logics. The research have been done by A. Baltag and S. Smets [4,5], F. Boge [8], V. Vilasini [22] and N. Nurgalieva [17]. Our study covers field of logic of correlated knowledge which is part of quantum modal logics.…”

Wigner\'s friend and quantum clocks

“…Interesting works such as one relating the FR Gedankenexperiment to Generalized Probability Theories (GPT) can be found in Vilasini, Nurgalieva and del Rio. 32 A disclaimer between the usually mistaken concepts of formalism and interpretation is made on Baumann and Wolf. 33 Philosphical digressions on the proper language used within the literature about this problem and an analysis of how much this problem could properly contribute to the evolution on the state-of-art of the measurement problem are shown in Hansen and Wolf.…”

“…Let us now transform the elements of the basis which constitutes f ij (t). Begining with f ij (t) = 1, 32) and with a simple change of variable u =…”

“…32) and because the eigenvalues of ρ(T ) and ρ(−T ) are always non-negative and lower or equal than 1, this limit automatically vanishes, resulting on the static equation[G[ρ], H] = 0. (3.33)…”