Completely real? A critical note on the claims by Colbeck and Renner

TL;DR

This paper critically examines claims that the quantum state fully describes future measurement outcomes, arguing that existing proofs are insufficient and that key assumptions are unjustified, thus challenging the completeness of quantum mechanics.

Contribution

The paper provides a critical analysis of Colbeck and Renner's claims, offering two partial supporting results and questioning the assumptions underlying their generalization.

Findings

No solid proof supports the claim of quantum state completeness.

Key assumptions in the proofs are found to be unsatisfactory.

Arguments for generalization rely on unjustified assumptions.

Abstract

In a series of papers Colbeck and Renner claim to have shown that the quantum state provides a complete description for the prediction of future measurement outcomes. In this paper I argue that thus far no solid satisfactory proof has been presented to support this claim. Building on the earlier work of Leifer, Landsman and Leegwater, I present and prove two results that only partially support this claim. I then discuss the arguments by Colbeck, Renner and Leegwater concerning how these results are to generalize to the full claim. This argument turns out to hinge on the implicit use of an assumption concerning the way unitary evolution is to be represented in any possible completion of quantum mechanics. I argue that this assumption is unsatisfactory and that possible attempts to validate it based on measurement theory also do not succeed.