# Multi-agent paradoxes beyond quantum theory

## TL;DR

This paper extends the Frauchiger-Renner paradox to generalized probabilistic theories, demonstrating that certain non-quantum theories like box world can also lead to logical contradictions when modeling observers' memories.

## Contribution

It generalizes the conditions for multi-agent paradoxes beyond quantum theory and applies them to GPTs, revealing contradictions in theories like box world with shared PR boxes.

## Key findings

- Contradictions found in box world with PR boxes
- Framework broadens understanding of paradoxes in physical theories
- Memory evolution modeled consistently with operational criteria

## 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, with a thought experiment that leads to a multi-agent paradox. 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 may evolve in box world, in a way consistent with Barrett's criteria for allowed operations.