Relational Quantum Mechanics is Still Incompatible with Quantum Mechanics

TL;DR

This paper demonstrates that Relational Quantum Mechanics remains incompatible with standard quantum mechanics by analyzing measurement outcomes on a GHZ state, and defends previous results against critiques.

Contribution

It provides a rigorous proof that relational facts conflict with quantum mechanics and addresses criticisms to reinforce this conclusion.

Findings

Relational facts are inconsistent with quantum mechanics.

The proof uses a GHZ state and sequential measurements.

Critiques of previous work are shown to be invalid.

Abstract

We showed in a recent article (Lawrence et. al., 2023, Quantum 7, 1015), that relative facts (outcomes), a central concept in Relational Quantum Mechanics, are inconsistent with Quantum Mechanics. We proved this by constructing a Wigner-Friend type sequential measurement scenario on a Greenberger-Horne-Zeilinger (GHZ) state of three qubits, and making the following assumption: "if an interpretation of quantum theory introduces some conceptualization of outcomes of a measurement, then probabilities of these outcomes must follow the quantum predictions as given by the Born rule." Our work has been criticized by Cavalcanti, Di Biagio, and Rovelli (CDR). In this note we show that their critique is invalid, and that their specific arguments raise questions of principle.