A possibilistic no-go theorem on the Wigner's friend paradox

Marwan Haddara, Eric G. Cavalcanti

Published 2022-05-24Version 1

In a recent work, Bong et al. [Nat. Phys. 16, 1199 (2020)] proved a no-go theorem demonstrating a contradiction between a set of assumptions called "Local Friendliness" (LF) and certain quantum phenomena on an extended version of the Wigner's friend scenario. The LF assumptions can be understood as the conjunction of two independent assumptions: Absoluteness of Observed Events (AOE) and Local Agency (LA). The proof of the LF theorem, however, implicitly assumes the validity of standard probability theory for dealing with sets of events that AOE implies to have simultaneously well-defined values. Here we present a probability-free version of the Local Friendliness theorem. The argument is phrased in the language of possibilities, which we make formal by using a modal logical approach. It relies on a slightly weaker version of Local Agency, which we call "Possibilistic Local Agency".