Quantum erasing the memory of Wigners friend

The Wigners friend paradox concerns one of the most puzzling problems of quantum mechanics: the consistent description of multiple nested observers. Recently, a variation of Wigners 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 Schrodinger 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 Renners 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 Wigners subsequent measurements. The first context may be seen as the quantum erasure of the memory of Wigners 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.