Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Extended Wigner's friend paradoxes do not require nonlocal correlations

Laurens Walleghem, Rafael Wagner, Yìlè Yīng, David Schmid

TL;DR

The paper shows that extended Wigner's friend paradoxes can arise from contextual correlations alone, not requiring Bell nonlocality. It constructs a five-measurement, single-system KCBS-style scenario embedded in an EWF setup with a superobserver, and derives a no-go theorem from Universality of Unitarity, Absoluteness of Observed Events, Possibilistic Born Rule, and Commutation Irrelevance. A concrete quantum realization and a generalization to n-cycle contextuality are provided, highlighting a contextual-origin paradox that challenges traditional assumptions about measurement and observation in quantum theory. The work illuminates the role of nonclassicality forms beyond nonlocality in quantum foundations and points to future device-independent and contextuality-focused directions for extended Wigner's friend arguments.

Abstract

Extended Wigner's friend no-go theorems provide a modern lens for investigating the measurement problem, by making precise the challenges that arise when one attempts to model agents as dynamical quantum systems. Most such no-go theorems studied to date, such as the Frauchiger-Renner argument and the Local Friendliness argument, are explicitly constructed using quantum correlations that violate Bell inequalities. In this work, we show that such correlations are not necessary for having extended Wigner's friend paradoxes, by constructing a no-go theorem utilizing a proof of the failure of noncontextuality. The argument hinges on a novel metaphysical assumption (which we term Commutation Irrelevance) that is a natural extension of a key assumption going into the Frauchiger and Renner's no-go theorem.

Extended Wigner's friend paradoxes do not require nonlocal correlations

TL;DR

The paper shows that extended Wigner's friend paradoxes can arise from contextual correlations alone, not requiring Bell nonlocality. It constructs a five-measurement, single-system KCBS-style scenario embedded in an EWF setup with a superobserver, and derives a no-go theorem from Universality of Unitarity, Absoluteness of Observed Events, Possibilistic Born Rule, and Commutation Irrelevance. A concrete quantum realization and a generalization to n-cycle contextuality are provided, highlighting a contextual-origin paradox that challenges traditional assumptions about measurement and observation in quantum theory. The work illuminates the role of nonclassicality forms beyond nonlocality in quantum foundations and points to future device-independent and contextuality-focused directions for extended Wigner's friend arguments.

Abstract

Extended Wigner's friend no-go theorems provide a modern lens for investigating the measurement problem, by making precise the challenges that arise when one attempts to model agents as dynamical quantum systems. Most such no-go theorems studied to date, such as the Frauchiger-Renner argument and the Local Friendliness argument, are explicitly constructed using quantum correlations that violate Bell inequalities. In this work, we show that such correlations are not necessary for having extended Wigner's friend paradoxes, by constructing a no-go theorem utilizing a proof of the failure of noncontextuality. The argument hinges on a novel metaphysical assumption (which we term Commutation Irrelevance) that is a natural extension of a key assumption going into the Frauchiger and Renner's no-go theorem.
Paper Structure (20 sections, 48 equations, 2 figures)

This paper contains 20 sections, 48 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Assumptions for EWF arguments
  3. The $5$-cycle noncontextuality scenario
  4. An EWF scenario with measurements on a single system
  5. No-go theorem
  6. Discussion and outlook
  7. How well motivated is Commutation Irrelevance?
  8. Why one can (but should not) justify Commutation Irrelevance using noncontextuality
  9. Why our argument does not appeal to the projection postulate
  10. Future directions.
  11. Kochen-Specker contextuality
  12. General framework
  13. An $n$-cycle logical contextual model
  14. Logically contextual $n$-cycle behaviour for odd and even $n$
  15. Turning an odd $n$-cycle paradox into an even $n$-cycle paradox and vice versa
  16. ...and 5 more sections

Figures (2)

  • Figure 1: Schematic depiction of the scenario. Five friends $A_1, \dots, A_5$ perform the five measurements from a 5-cycle noncontextuality no-go theorem on a system $S$, while a superobserver Wigner undoes the first three of these measurements at particular times in between. Each measurement $M_i$ is modeled unitarily as $U_{M_i}$, following the assumption of Universality of Unitarity. The unitaries from $U_{M_2}$ to $U^{\dagger}_{M_3}$ are collectively denoted as $U$. In each measurement $M_i$, agent $A_i$ obtains an absolute outcome $a_i$, following the assumption of Absoluteness of Observed Events.
  • Figure 2: $n$-cycle compatibility hypergraphs. Cycle graphs $C_n$ for $n=3,4,5,6$. Each graph defines a compatibility structure that can be associated with measurement scenarios. Graph $C_4$ depicts the compatibility structure of the bipartite Bell scenarios leading to the Clauser-Horne-Shimony-Holt (CHSH) inequality clauser1969proposed. Graph $C_5$ depicts the compatibility structure leading to the Klyachko-Can-Binicioğlu-Shumovsky (KCBS) inequality klyachko2008simple.