Any theory that admits a Wigner's Friend type multi-agent paradox is logically contextual

Abstract

39+16 pages. Both authors contributed equally to this work. Initial versions of some of these results were included in NN's PhD thesis (ETH Zurich, 2023)Wigner's Friend scenarios push the boundaries of quantum theory by modeling agents, along with their memories storing measurement outcomes, as physical quantum systems. Extending these ideas beyond quantum theory, we ask: in which physical theories, and under what assumptions, can agents who are reasoning logically about each other's measurement outcomes encounter apparent paradoxes? To address this, we prove a link between Wigner's Friend type multi-agent paradoxes and contextuality in general theories: if agents who are modeled within a physical theory come to a contradiction when reasoning using that theory (under certain assumptions on how they reason and describe measurements), then the theory must admit contextual correlations of a logical form. This also yields a link between the distinct fundamental concepts of Heisenberg cuts and measurement contexts in general theories, and in particular, implies that the quantum Frauchiger-Renner paradox is a proof of logical contextuality. Moreover, we identify structural properties of such paradoxes in general theories and specific to quantum theory. For instance, we demonstrate that theories admitting behaviors corresponding to extremal vertices of n-cycle contextuality scenarios admit Wigner's Friend type paradoxes without post-selection, and that any quantum Wigner's Friend paradox based on the n-cycle scenario must necessarily involve post-selection. Further, we construct a multi-agent paradox based on a genuine contextuality scenario involving sequential measurements on a single system, showing that Bell non-local correlations between distinct subsystems are not necessary for Wigner's Friend paradoxes. Our work offers an approach to investigate the structure of physical theories and their information-theoretic resources by means of deconstructing the assumptions underlying multi-agent physical paradoxes