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

Abstract

The famous "Wigner's friend" paradox highlights the difficulty of modelling the evolution of quantum systems under measurement in situations where observers themselves are considered to be subject to the laws of quantum mechanics. In recent years, variations of the original Wigner's friend paradox have been recognized as fruitful arenas for probing the foundations of quantum theory. In particular Bong et al. [Nature Physics 16, 1199 (2020)] demonstrated a contradiction between a set of intuitive assumptions called "Local Friendliness" (LF) and certain quantum phenomena on an extended version of the Wigner's friend paradox. The LF assumptions can be understood as the conjunction of two independent assumptions: Absoluteness of Observed Events requires that any event observed by any observer has an absolute, rather than relative, value; Local Agency is the assumption that an intervention cannot be correlated with relevant events outside its future light cone. These assumptions are weaker than the assumptions that lead to Bell's theorem, and thus while the Local Friendliness result may be considered to be conceptually comparable to Bell's result, its implications are even deeper. The proof of the LF no-go theorem, however, relies on probability theory, and a fundamental question remained whether or not LF is an inherently statistical concept. Here we present a probability-free version of the Local Friendliness theorem, building upon Hardy's no-go theorem for local hidden variables. The argument is phrased in the language of possibilities, which we make formal by using a modal logical approach. It relies on a weaker version of Local Agency, which we call "Possibilistic Local Agency": the assumption that an intervention cannot affect the possibilities of events outside its future light cone.

Allowing Wigner’s friend to sequentially measure incompatible observables

“…He considered an assumption he called 'observer-independent facts', along with the previously established assumptions such as locality and freedom of choice, although not predetermination [2]. Other works have further developed the ideas proposed in [2], with analyses considering different assumptions and/or scenarios [3][4][5][6][7][8]. A review of such results is given in [9].…”