A refined Frauchiger–Renner paradox based on strong contextuality
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AbstractThe Frauchiger–Renner paradox derives an inconsistency when quantum theory is used to describe the use of itself, by means of a scenario where agents model other agents quantumly and reason about each other's knowledge. We observe that logical contextuality (à la Hardy) is the key ingredient of the FR paradox, and we provide a stronger paradox based on the strongly contextual GHZ–Mermin scenario. In contrast to the FR paradox, this GHZ–FR paradox neither requires post-selection nor any reasoning by observers who are modelled quantumly. If one accepts the universality of quantum theory including superobservers, we propose a natural extension of Peres's dictum to resolve these extended Wigner's friend paradoxes.Featured image: Schematical representation of the FR paradox (a), which is based on two-party Bell nonlocality, and the refined FR paradox (b), which is based on the three-party strongly nonlocal GHZ–Mermin model.Popular summaryDespite its empirical success and predictive power, quantum theory has long been overshadowed by the measurement problem, often illustrated by a thought experiment known as "Schrödinger's cat." The cat is initially placed in a box that contains a physical contraption governed by the laws of quantum theory, which may or may not kill the cat after a certain time. Ending up in a quantum superposition, the cat seems to be alive and dead at the same time. However, upon opening the box, we will always find the cat either dead or alive. Wigner sharpened this paradox by replacing the cat in the box with an observer known as "Wigner's friend" who resides in a sealed lab that Wigner models as a quantum system. The friend measures a quantum system and claims to obtain a single-valued outcome, while Wigner describes his friend as being in a superposition of seeing different outcome values. It is only when Wigner asks his friend for her result that he ascribes it a definite outcome value. But what causes the wave function to collapse from a superposition to a single-valued outcome, and how? In the last decade, such foundational puzzles have been revisited by extending Wigner's thought experiment to involve multiple friends performing measurements, with the Frauchiger–Renner paradox as a particularly influential example. These arguments combine Wigner's thought experiment with another puzzling aspect of quantum theory, nonlocality, famously referred to as `spooky action at a distance' by Einstein. In this work, we present a stronger version of the Frauchiger–Renner paradox. Our scenario involves multiple observers who formulate simple predictions using quantum theory and derive a contradiction when combining their knowledge. We discuss a potential resolution based on the idea that nature is built out of relations rather than absolutes.► BibTeX data@article{Walleghem2026refined, doi = {10.22331/q-2026-05-26-2116}, url = {https://doi.org/10.22331/q-2026-05-26-2116}, title = {A refined {F}rauchiger–{R}enner paradox based on strong contextuality}, author = {Walleghem, Laurens and Barbosa, Rui Soares and Pusey, Matthew F. and Weigert, Stefan}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2116}, month = may, year = {2026} }► References [1] D. Frauchiger and R. Renner, Quantum theory cannot consistently describe the use of itself, Nat. 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Galvão, Inequalities witnessing coherence, nonlocality, and contextuality, Phys. Rev. A 109, 032220 (2024). https://doi.org/10.1103/physreva.109.032220Cited byCould not fetch Crossref cited-by data during last attempt 2026-05-26 07:18:16: Could not fetch cited-by data for 10.22331/q-2026-05-26-2116 from Crossref. This is normal if the DOI was registered recently. Could not fetch ADS cited-by data during last attempt 2026-05-26 07:18:22: Cannot retrieve data from ADS due to rate limitations.This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions. AbstractThe Frauchiger–Renner paradox derives an inconsistency when quantum theory is used to describe the use of itself, by means of a scenario where agents model other agents quantumly and reason about each other's knowledge. We observe that logical contextuality (à la Hardy) is the key ingredient of the FR paradox, and we provide a stronger paradox based on the strongly contextual GHZ–Mermin scenario. In contrast to the FR paradox, this GHZ–FR paradox neither requires post-selection nor any reasoning by observers who are modelled quantumly. If one accepts the universality of quantum theory including superobservers, we propose a natural extension of Peres's dictum to resolve these extended Wigner's friend paradoxes.Featured image: Schematical representation of the FR paradox (a), which is based on two-party Bell nonlocality, and the refined FR paradox (b), which is based on the three-party strongly nonlocal GHZ–Mermin model.Popular summaryDespite its empirical success and predictive power, quantum theory has long been overshadowed by the measurement problem, often illustrated by a thought experiment known as "Schrödinger's cat." The cat is initially placed in a box that contains a physical contraption governed by the laws of quantum theory, which may or may not kill the cat after a certain time. Ending up in a quantum superposition, the cat seems to be alive and dead at the same time. However, upon opening the box, we will always find the cat either dead or alive. Wigner sharpened this paradox by replacing the cat in the box with an observer known as "Wigner's friend" who resides in a sealed lab that Wigner models as a quantum system. The friend measures a quantum system and claims to obtain a single-valued outcome, while Wigner describes his friend as being in a superposition of seeing different outcome values. It is only when Wigner asks his friend for her result that he ascribes it a definite outcome value. But what causes the wave function to collapse from a superposition to a single-valued outcome, and how? In the last decade, such foundational puzzles have been revisited by extending Wigner's thought experiment to involve multiple friends performing measurements, with the Frauchiger–Renner paradox as a particularly influential example. These arguments combine Wigner's thought experiment with another puzzling aspect of quantum theory, nonlocality, famously referred to as `spooky action at a distance' by Einstein. In this work, we present a stronger version of the Frauchiger–Renner paradox. Our scenario involves multiple observers who formulate simple predictions using quantum theory and derive a contradiction when combining their knowledge. We discuss a potential resolution based on the idea that nature is built out of relations rather than absolutes.► BibTeX data@article{Walleghem2026refined, doi = {10.22331/q-2026-05-26-2116}, url = {https://doi.org/10.22331/q-2026-05-26-2116}, title = {A refined {F}rauchiger–{R}enner paradox based on strong contextuality}, author = {Walleghem, Laurens and Barbosa, Rui Soares and Pusey, Matthew F. and Weigert, Stefan}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {10}, pages = {2116}, month = may, year = {2026} }► References [1] D. Frauchiger and R. Renner, Quantum theory cannot consistently describe the use of itself, Nat. Commun. 9, 3711 (2018). https://doi.org/10.1038/s41467-018-05739-8 [2] E. P. Wigner, Remarks on the mind-body question, in The Scientist Speculates, edited by I. J. 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