Quantum erasing the memory of Wigner’s friend

Cyril Elouard1,2, Philippe Lewalle1, Sreenath K. Manikandan1, Spencer Rogers1, Adam Frank1, and Andrew N. Jordan1,3

1Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA
2QUANTIC lab, INRIA, 2 Rue Simone IFF, 75012 Paris, France
3Institute for Quantum Studies, Chapman University, Orange, CA 92866, USA

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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.

In quantum mechanics, observation affects the measured system. But what happens if the system includes an observer doing a quantum measurement themselves? This puzzling situation is the subject of the thought experiment known as Wigner’s Friend. A recent variation of this scenario raised questions about the range of validity of quantum mechanics, showing that multiple observers may obtain contradictory conclusions when reasoning with each other’s points of view.
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.

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[2] Shubhayan Sarkar and Debashis Saha, "Demonstration of quantum correlations that are incompatible with absoluteness of measurement", Physical Review A 107 2, 022226 (2023).

[3] Lídia del Rio and Renato Renner, "Reply to: Quantum mechanical rules for observed observers and the consistency of quantum theory", Nature Communications 15 1, 3024 (2024).

[4] Alexandru Baltag and Sonja Smets, "Logic Meets Wigner’s Friend (and their Friends)", International Journal of Theoretical Physics 63 4, 97 (2024).

[5] Veronika Baumann, "Classical Information and Collapse in Wigner’s Friend Setups", Entropy 25 10, 1420 (2023).

[6] Joseph M. Renes, "Consistency in the description of quantum measurement: Quantum theory can consistently describe the use of itself", arXiv:2107.02193, (2021).

[7] Dmitri Sokolovski and Alexandre Matzkin, "Wigner's Friend Scenarios and the Internal Consistency of Standard Quantum Mechanics", Entropy 23 9, 1186 (2021).

[8] Varun Narasimhachar, "Agents governed by quantum mechanics can use it intersubjectively and consistently", arXiv:2010.01167, (2020).

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