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.
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