Wigner's Friend Depends on Self-Contradictory Quantum Amplification

TL;DR

The paper demonstrates that Wigner's Friend scenario leads to a logical contradiction when assuming quantum amplification without collapse, showing the incompatibility of reversible measurement with macroscopic pointer states.

Contribution

It validates previous results and identifies the contradiction arising from assuming quantum amplification without collapse in a simple measurement experiment.

Findings

Reversible quantum amplification can lead to uncorrelated macroscopic pointer states.

The notion of reversible measurement is logically inconsistent with macroscopic pointer states.

Wigner's Friend scenario depends on self-contradictory assumptions about measurement and amplification.

Abstract

In a recent paper, \.Zukowski and Markiewicz showed that Wigner's Friend (and, by extension, Schr\"odinger's Cat) can be eliminated as physical possibilities on purely logical grounds. I validate this result and demonstrate the source of the contradiction in a simple experiment in which a scientist S attempts to measure the position of object $|O\rangle = |A\rangle_S + |B\rangle_S$ by using measuring device M chosen so that $|A\rangle_M \approx |A\rangle_S$ and $|B\rangle_M \approx |B\rangle_S$. I assume that the measurement occurs by quantum amplification without collapse, in which M can entangle with O in a way that remains reversible by S for some nonzero time period. This assumption implies that during this "reversible" time period, $|A\rangle_M \neq |A\rangle_S$ and $|B\rangle_M \neq |B\rangle_S$ -- i.e., the macroscopic pointer state to which M evolves is uncorrelated to the position of O relative to S. When the scientist finally observes the measuring device, its macroscopic pointer state is uncorrelated to the object in position $|A\rangle_S$ or $|B\rangle_S$, rendering the notion of "reversible measurement" a logical contradiction.