Quantum erasing the memory of Wigner's friend

TL;DR

This paper examines the Wigner's friend paradox by proposing a quantum erasure approach that clarifies the conflicting assumptions about observers and measurements in quantum mechanics.

Contribution

It introduces a necessary condition for a quantum system to act as an observer and presents a simple interferometric setup to analyze the paradox.

Findings

The three conflicting properties are associated with non-commuting observables.

The properties do not hold simultaneously, resolving the paradox.

The approach clarifies the assumptions leading to the paradox.

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 Schr\"odinger 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.