Abstract
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.
Highlights
In his famous gedankenexperiment, Wigner analyzes a setup in which a “super-observer” is assumed to be able to measure a whole lab, containing a human being, in any basis [1]
Paradoxical conclusions may emerge from such situations due to the tension between the rules of evolution for isolated quantum systems, which in principle can be applied at any scale, and the need for the projection postulate to describe measurements performed by observers
The measurement an observer O performs on a quantum system is well described by the measurement postulate, which attributes a well-defined outcome to the measurement and asserts that the measured system is projected into the corresponding eigenstate of the measured observable
Summary
Wigner analyzes a setup in which a “super-observer” is assumed to be able to measure a whole lab, containing a human being (a friend of his), in any basis [1]. By focusing on the role of memory, projection, and unitary evolution, we make explicit limits in the Wigner’s Friend paradox and the mechanism of quantum measurement, and provide an operational prescription to identify devices behaving as an observer. This discussion is useful in light of the recent related No-Go theorem of [16] that sought to illuminate key issues in quantum interpretation. Has been examined [17] to introduce an experiment distinguishing between Everett’s and the Copenhagen formulations of quantum mechanics, and recently to shed new light on the original Wigner’s friend scenario [18]
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