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In a recent work, Bong et al. [Nature Physics 16, 1199 (2020)] proved a no-gotheorem demonstrating a contradiction between a set of assumptions called"Local Friendliness" (LF) and certain quantum phenomena on an extended versionof the "Wigner's friend" paradox. The LF assumptions can be understood as theconjunction of two independent assumptions: Absoluteness of Observed Events(AOE) requires that events observed by any observer have absolute, rather thanrelative, values; Local Agency (LA) encodes the assumption that an interventioncannot influence events outside its future light cone. The proof of the LFno-go theorem, however, implicitly assumes the validity of standard probabilitytheory. Here we present a probability-free version of the Local Friendlinesstheorem, building upon Hardy's no-go theorem for local hidden variables. Theargument is phrased in the language of possibilities, which we make formal byusing a modal logical approach. It relies on a weaker version of Local Agency,which we call "Possibilistic Local Agency": the assumption that an interventioncannot influence the possibilities of events outside its future light cone.

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