Is the quantum state real? An extended review of $\psi$-ontology theorems
M. S. Leifer

TL;DR
This review comprehensively discusses the Pusey--Barrett--Rudolph Theorem, its implications for the reality of the quantum state, and related arguments, highlighting the debate over whether the quantum state is ontic or epistemic.
Contribution
It provides a detailed explanation of the Pusey--Barrett--Rudolph Theorem, its assumptions, improvements, criticisms, and compares it with other arguments regarding the nature of the quantum state.
Findings
The Pusey--Barrett--Rudolph Theorem strongly constrains realist interpretations of quantum mechanics.
Arguments by Hardy and Colbeck-Renner are less compelling than PBR's assumptions.
Open questions remain about the epistemic interpretations of the quantum state.
Abstract
Towards the end of 2011, Pusey, Barrett and Rudolph derived a theorem that aimed to show that the quantum state must be ontic (a state of reality) in a broad class of realist approaches to quantum theory. This result attracted a lot of attention and controversy. The aim of this review article is to review the background to the Pusey--Barrett--Rudolph Theorem, to provide a clear presentation of the theorem itself, and to review related work that has appeared since the publication of the Pusey--Barrett--Rudolph paper. In particular, this review: Explains what it means for the quantum state to be ontic or epistemic (a state of knowledge); Reviews arguments for and against an ontic interpretation of the quantum state as they existed prior to the Pusey--Barrett--Rudolph Theorem; Explains why proving the reality of the quantum state is a very strong constraint on realist theories in that it…
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