The Wigner's friend paradox concerns one of the most puzzling problems of quantum mechanics: the consistent description of multiple nested observers. Recently, a variation of Wigner's gedankenexperiment, introduced by Frauchiger and Renner, has lead to new debates about the self-consistency of quantum mechanics. At the core of the paradox lies the description of an observer and the object it measures as a closed system obeying the Schrödinger equation. We revisit this assumption to derive a necessary condition on a quantum system to behave as an observer. We then propose a simple single-photon interferometric setup implementing Frauchiger and Renner's scenario, and use the derived condition to shed a new light on the assumptions leading to their paradox. From our description, we argue that the three apparently incompatible properties used to question the consistency of quantum mechanics correspond to two logically distinct contexts: either one assumes that Wigner has full control over his friends' lab, or conversely that some parts of the labs remain unaffected by Wigner's subsequent measurements. The first context may be seen as the quantum erasure of the memory of Wigner's friend. We further show these properties are associated with observables which do not commute, and therefore cannot take well-defined values simultaneously. Consequently, the three contradictory properties never hold simultaneously.
Here, we gain new insights into this situation by showing that the conclusions involved in the paradox are actually drawn from two incompatible experimental contexts, and are therefore never realized simultaneously. To make this clear, we propose a simplification of the thought experiment involving a single-photon interferometer, in which the two different experimental setups are transparent. In addition, we relate these two setups to the capacity of the agent to behave as an observer – able of doing a measurement – or not, which we identify with the presence of a stable memory in which the measurement outcome can be stored. Without assuming the measurement postulate, our approach provides an operational framework to distinguish systems behaving as observers from those which must be modelled with the Schrödinger equation.
 Wigner, E. P. Remarks on the Mind-Body Question. In Symmetries and Reflections, 171–184 (Indiana University Press, 1967). URL https://doi.org/10.1007/978-3-642-78374-6_20.
 Heisenberg, W. The Physical Principles of the Quantum Theory (University of Chicago Press, Chicago, 1930). URL https://doi.org/10.1007/978-3-642-61742-3_10.
 Frauchiger, D. & Renner, R. Quantum theory cannot consistently describe the use of itself. Nat. Commun. 9, 1–10 (2018). URL https://doi.org/10.1038/s41467-018-05739-8.
 Nurgalieva, N. & del Rio, L. Inadequacy of modal logic in quantum settings. In Selinger, P. & Chiribella, G. (eds.) Proceedings of the 15th International Conference on Quantum Physics and Logic, Halifax, Canada, 3-7th June 2018, vol. 287 of Electronic Proceedings in Theoretical Computer Science, 267–297 (Open Publishing Association, 2019). URL https://doi.org/10.4204/EPTCS.287.16.
 Lazarovici, D. & Hubert, M. How Quantum Mechanics can consistently describe the use of itself. Sci. Rep. 9, 1–8 (2019). URL https://doi.org/10.1038/s41598-018-37535-1.
 Waaijer, M. & van Neerven, J. Relational analysis of the Frauchiger–Renner paradox and existence of records from the past. arXiv (2019). URL https://arxiv.org/abs/1902.07139v1. 1902.07139.
 Baumann, V. & Wolf, S. On Formalisms and Interpretations. Quantum 2, 99 (2018). 1710.07212v6. URL https://doi.org/10.22331/q-2018-10-15-99.
 Krismer, R. Representation Lost: The Case for a Relational Interpretation of Quantum Mechanics. Entropy 20, 975 (2018). URL https://doi.org/10.3390/e20120975.
 Losada, M., Laura, R. & Lombardi, O. Frauchiger-Renner argument and quantum histories. Phys. Rev. A 100, 052114 (2019). URL https://doi.org/10.1103/PhysRevA.100.052114.
 Nurgalieva, Nuriya & Renner, Renato, Testing quantum theory with thought experiments. Contemp. Phys. 61, 193–216 (2020). URL https://doi.org/10.1080/00107514.2021.1880075.
 Matzkin, A. & Sokolovski, D. Wigner's friend, Feynman's paths and material records. EPL 131, 40001 (2020). URL https://doi.org/10.1209/0295-5075/131/40001.
 von Neumann, J. Mathematical Foundations of Quantum Mechanics (Princeton University Press, Princeton, New Jersey, 1955).
 Scully, M. O. & Drühl, K. Quantum eraser: A proposed photon correlation experiment concerning observation and "delayed choice" in quantum mechanics. Phys. Rev. A 25, 2208–2213 (1982). URL https://doi.org/10.1103/PhysRevA.25.2208.
 Kim, Y.-H., Yu, R., Kulik, S. P., Shih, Y. & Scully, M. O. Delayed ''Choice'' Quantum Eraser. Phys. Rev. Lett. 84, 1–5 (2000). URL https://doi.org/10.1103/PhysRevLett.84.1.
 Walborn, S. P., Terra Cunha, M. O., Pádua, S. & Monken, C. H. Double-slit quantum eraser. Phys. Rev. A 65, 033818 (2002). URL https://doi.org/10.1103/PhysRevA.65.033818.
 Hardy, L. Quantum mechanics, local realistic theories, and Lorentz-invariant realistic theories. Phys. Rev. Lett. 68, 2981–2984 (1992). URL https://doi.org/10.1103/PhysRevLett.68.2981.
 Bohr, N. The causality problem in atomic physics. In New Theories in Physics, 11–30 (International Institute of Intellectual Cooperation, Warsaw, 1939). URL https://doi.org/10.1016/S1876-0503(08)70376-1.
 Bub, J. `Two Dogmas' Redux. In Orly Shenker and Meir Hemmo (eds), Quantum, Probability, Logic: The Work and Influence of Itamar Pitowsky, 199-–215 (Springer, 2020). URL https://doi.org/10.1007/978-3-030-34316-3. 1907.06240.
 Bub, J. & Pitowsky, I. Two dogmas about quantum mechanics. In Simon Saunders, Jonathan Barrett, Adrian Kent, and David Wallace (eds), Many Worlds?: Everett, Quantum Theory, and Reality (Oxford Scholarship Online, 2010). URL https://doi.org/10.1093/acprof:oso/9780199560561.003.0016. 0712.4258.
 Fuchs, C. A. & Stacey, B. C. QBism: Quantum Theory as a Hero's Handbook. In Ernst M. Rasel, Wolfgang P. Schleich, Sabine Wölk (eds), Proceedings of the International School of Physics "Enrico Fermi": Foundations of Quantum Theory, 133-–202 (IOS Press, 2019). URL https://doi.org/10.3254/978-1-61499-937-9-133. 1612.07308.
 Varun Narasimhachar, "Agents governed by quantum mechanics can use it intersubjectively and consistently", arXiv:2010.01167.
 Dmitri Sokolovski and Alexandre Matzkin, "Wigner's Friend Scenarios and the Internal Consistency of Standard Quantum Mechanics", Entropy 23 9, 1186 (2021).
 Joseph M. Renes, "Consistency in the description of quantum measurement: Quantum theory can consistently describe the use of itself", arXiv:2107.02193.
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