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

Kok-Wei Bong,Howard M Wiseman,Eric G Cavalcanti,Yeong-Cherng Liang,Nora Tischler,Geoff J Pryde,Aníbal Utreras-Alarcón,Farzad Ghafari

doi:10.1038/s41567-020-0990-x

Abstract

Does quantum theory apply at all scales, including that of observers? New light on this fundamental question has recently been shed through a resurgence of interest in the long-standing Wigner's friend paradox. This is a thought experiment addressing the quantum measurement problem -- the difficulty of reconciling the (unitary, deterministic) evolution of isolated systems and the (non-unitary, probabilistic) state update after a measurement. Here, by building on a scenario with two separated but entangled friends introduced by Brukner, we prove that if quantum evolution is controllable on the scale of an observer, then one of 'No-Superdeterminism', 'Locality' or 'Absoluteness of Observed Events' -- that every observed event exists absolutely, not relatively -- must be false. We show that although the violation of Bell-type inequalities in such scenarios is not in general sufficient to demonstrate the contradiction between those three assumptions, new inequalities can be derived in a theory-independent manner, that are violated by quantum correlations. This is demonstrated in a proof-of-principle experiment where a photon's path is deemed an observer. We discuss how this new theorem places strictly stronger constraints on physical reality than Bell's theorem.

Highlights

Wigner’s friend[1] is a thought experiment that illustrates what is perhaps the thorniest foundational problem in quantum theory: the measurement problem[2,3]
Already for a slightly more complicated extended Wigner’s friend scenario (EWFS) with three binary-outcome measurement choices per superobserver, we show that the set of Local Friendliness (LF) correlations is a strict superset of the set of Local Hidden Variable (LHV) correlations
We have proven a new theorem, namely that the joint assumption of Absoluteness of Observed Events, Locality and NoSuperdeterminism is incompatible with the empirical predictions of quantum mechanics if one observer (a “superobserver”) can manipulate the quantum state ascribed to another observer (a “friend”)

Summary

Introduction

Wigner’s friend[1] is a thought experiment that illustrates what is perhaps the thorniest foundational problem in quantum theory: the measurement problem[2,3]. The problem is how to reconcile the two rules for state evolution found in every textbook on quantum mechanics: the (unitary, deterministic) evolution of isolated systems, and the (non-unitary, probabilistic) state update after a measurement (the “collapse” of the wave function). In accordance with the state-update rule, the friend assigns the eigenstate corresponding to their observed outcome to decoherence can “save the appearances” by explaining the suppression of quantum effects at the macroscopic level, it cannot solve the measurement problem: “We are still left with a multitude of (albeit individually well-localized quasiclassical) components of the wave function, and we need to supplement or otherwise to interpret this situation in order to explain why and how single outcomes are perceived”[2]. We rigorously demonstrate that radical revisions of such types are required

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