PBR theorem and Einstein's quantum hole argument

TL;DR

This paper explores the PBR theorem in quantum mechanics, analyzing its connection to Einstein's earlier arguments on quantum incompleteness and the philosophical implications of quantum state reality.

Contribution

It provides a comparative analysis of the PBR theorem and Einstein's quantum hole argument, highlighting their conceptual similarities and differences.

Findings

The PBR theorem supports the reality of the quantum state.

Einstein's quantum hole argument shares conceptual roots with the PBR theorem.

The paper clarifies the philosophical implications of quantum state interpretations.

Abstract

Upon reading Einstein's views on quantum incompleteness in publications or in his correspondence after 1935 (the EPR paradox), one gets a very intense feeling of deja-vu. Einstein presents a quantum hole argument, which somewhat reminds of the hole argument in his 1914 "Entwurf" theory of general relativity. PBR write in their paper, "An important step towards the derivation of our result is the idea that the quantum state is physical if distinct quantum states correspond to non-overlapping distributions for [physical states]". PBR then conclude, "The general notion that two distinct quantum states may describe the same state of reality, however, has a long history. For example, in a letter to Schr\"odinger containing a variant of the famous EPR (Einstein-Podolsky-Rosen) argument", and they refer to Einstein's quantum hole argument. This short paper discusses the PBR theorem, and the connection between the PBR argument and Einstein's argument and solution.