Connecting extended Wigner's friend arguments and noncontextuality

Laurens Walleghem; Yìlè Yīng; Rafael Wagner; David Schmid

doi:10.22331/q-2025-07-31-1819

Connecting extended Wigner’s friend arguments and noncontextuality

Laurens Walleghem^1,2, Yìlè Yīng^3,4, Rafael Wagner^5,2,6,7, and David Schmid⁸

¹Department of Mathematics, University of York, Heslington, York YO10 5DD, United Kingdom
²International Iberian Nanotechnology Laboratory (INL), Av. Mestre José Veiga, 4715-330 Braga, Portugal
³Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada, N2L 2Y5
⁴Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1
⁵Institute of Theoretical Physics, Ulm University, Albert-Einstein-Allee 11 89081, Ulm, Germany
⁶Centro de Física, Universidade do Minho, Braga 4710-057, Portugal
⁷Department of Physics ``E. Fermi'', University of Pisa, Largo B. Pontecorvo 3, 56127 Pisa, Italy
⁸International Centre for Theory of Quantum Technologies, University of Gdańsk, 80-309 Gdańsk, Poland

Published:	2025-07-31, volume 9, page 1819
Editor:	Cyril Branciard
Eprint:	arXiv:2409.07537v2
Doi:	https://doi.org/10.22331/q-2025-07-31-1819
Citation:	Quantum 9, 1819 (2025).

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Abstract

The Local Friendliness argument is an extended Wigner's friend no-go theorem that provides strong constraints on the nature of reality – stronger even than those imposed by Bell's theorem or by noncontextuality arguments. In this work, we prove a variety of connections between Local Friendliness scenarios and Kochen-Specker noncontextuality. Specifically, we first show how one can derive new Local Friendliness inequalities using known tools and results from the literature on Kochen-Specker noncontextuality. In doing so, we provide a new derivation for some of the facets of the Local Friendliness polytope, and we prove that this polytope is equal to the Bell polytope in a wide range of extended Wigner's friend scenarios with multipartite agents and sequential measurements. We then show how any possibilistic Kochen-Specker argument can be mathematically translated into a related proof of the Local Friendliness no-go theorem. In particular, we construct a novel kind of Local Friendliness scenario where a friend implements several compatible measurements (or joint measurements of these) in between the superobserver's operations on them. We illustrate this with the well-known 5-cycle and Peres-Mermin contextuality arguments.

Featured image: The 5-cycle KCBS contextuality argument (with compatibility graph of (a)) is used in our Extended Wigner's Friend scenario (shown in (b)) to violate the Local Friendliness assumptions. Alice's friends (left part of (b)) perform the measurements of the 5-cycle argument (with "undoings" by superobserver Alice in between). All 5-cycle contexts can be directly obtained by Alice and her friends—except for $A_1-A_5$, as the measurement outcome of $A_1$ by friend 1 is already erased by Alice when friend 5 performs their measurement. Therefore, to obtain a contradiction based on 5-cycle contextuality, friend 1 encodes her outcome in a qubit maximally entangled with Bob, so that the $A_1,A_5$ context can also be accessed empirically.

Popular summary

The Wigner's friend argument aims to illuminate the measurement problem by considering what happens when an agent's measurement is modeled as a unitary interaction. The Local Friendliness argument is an extension of the Wigner's friend argument that provides strong constraints on the nature of reality—stronger even than those imposed by Bell's theorem or by noncontextuality arguments. In this work, we prove a variety of connections between Local Friendliness scenarios and Kochen-Specker noncontextuality, which is a well-studied assumption that can be motivated by Leibniz's principle. Specifically, we show how one can derive new Local Friendliness inequalities using known tools and results from the literature on Kochen-Specker noncontextuality, and we prove that the resulting polytope is equal to the Bell polytope in a wide range of scenarios. We then show how any possibilistic Kochen-Specker argument can be mathematically translated into a related proof of the Local Friendliness no-go theorem. In particular, we construct a novel kind of Local Friendliness scenario where a friend implements several compatible measurements (or joint measurements of these) in between the superobserver's operations on them. We illustrate this with the well-known 5-cycle and Peres-Mermin contextuality arguments.

► BibTeX data

@article{Walleghem2025connectingextended,
  doi = {10.22331/q-2025-07-31-1819},
  url = {https://doi.org/10.22331/q-2025-07-31-1819},
  title = {Connecting extended {W}igner's friend arguments and noncontextuality},
  author = {Walleghem, Laurens and Yīng, Y{\`{i}}l{\`{e}} and Wagner, Rafael and Schmid, David},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1819},
  month = jul,
  year = {2025}
}

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[2] Laurens Walleghem, Rui Soares Barbosa, Matthew F. Pusey, and Stefan Weigert, "A refined Frauchiger–Renner paradox based on strong contextuality", Quantum 10, 2116 (2026).

[3] Laurens Walleghem, Rafael Wagner, Yìlè Yīng, and David Schmid, "Extended Wigner's friend paradoxes do not require nonlocal correlations", Physical Review A 112 2, 022212 (2025).

[4] Marwan Haddara and Eric G. Cavalcanti, "Local friendliness polytopes in multipartite scenarios", Physical Review A 111 1, 012206 (2025).

[5] Rafael Wagner, "Coherence and contextuality as quantum resources", arXiv:2511.16785, (2025).

[6] Nuriya Nurgalieva and V. Vilasini, "Any theory that admits a Wigner's Friend type multi-agent paradox is logically contextual", arXiv:2502.03874, (2025).

[7] Laurens Walleghem, "Wigner's friend's black hole adventure: an argument for complementarity?", arXiv:2507.05369, (2025).

[8] Marwan Haddara, Howard M. Wiseman, and Eric G. Cavalcanti, "Properties and Applications of Partially Deterministic Polytopes", arXiv:2510.25127, (2025).

[9] Tom Rivlin, Sophie Engineer, and Veronika Baumann, "Emergence of Classicality in Wigner's Friend Scenarios", arXiv:2507.21221, (2025).

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