Multi-agent paradoxes beyond quantum theory

V. Vilasini (University of York), Nuriya Nurgalieva (ETH Zurich), Lídia Del Rio (ETH Zurich)

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. 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). 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, which is stronger than the quantum paradox, in that it does not rely on post-selection. 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 evolve in box world, in away consistent with Barrett’s criteria for allowed operations.