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arXiv:1202.6465 · Physical Review A

Alternative experimental protocol to demonstrate the Pusey-Barrett-Rudolph theorem

D. J. Miller

Published Jan 16, 2013• 13 citations
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Abstract

Pusey, Barrett, and Rudolph (PBR) have recently proven an important new theorem in the foundations of quantum mechanics [Pusey et al., Nature Phys. 8, 475 (2012)]. Here we propose alternative experimental protocols which lead to the PBR result for a special case and a weaker PBR-like result generally. Alternative experimental protocols support the assumption of measurement independence required for the PBR theorem.

DOI
10.1103/physreva.87.014103

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Can quantum mechanics be considered as statistical?(comment)

Aurélien Drezet

This is a short manuscript which was initially submitted to Nature Physics as a comment to the PBR (Pusey, M. F., Barrett, J., Rudolph, T) paper just after its publication in 2012. The comment was not accepted. I however think that the argumentation is correct: one is free to judge!

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We review the Pusey-Barret-Rudolph (PBR) theorem\cite{PBR} and their setup, and arrive to the conclusion that the reality of a quantum state $ψ$ is intrinsically attached to the measurement the system described by $ψ$ has undergone. We show that a state that has not been measured can be regarded as pure information, while a state that has been measured has to be regarded as a physical property of a certain system, having a counterpart in reality. This demonstration implies that the statement of PBR's theorem changes in a meaningful way.

arXiv:1810.11072•Oct 25, 2018•0 citations
Pusey, Barrett, and Rudolph (PBR) have recently proven an important new theorem in the foundations of quantum mechanics [Pusey et al., Nature Phys. 8, 475 (2012)]. Here we propose alternative experimental protocols which lead to the PBR result for a special case and a weaker PBR-like result generally. Alternative experimental protocols support the assumption of measurement independence required for the PBR theorem.
Pusey, Barrett and Rudolph (PBR) have recently given a completely novel argument that restricts the class of possible models for quantum phenomena (arXiv:1111.3328). In these notes the assumptions used by PBR are considerably weakened, to further restrict the class of possible models. The `factorisability' assumption used by PBR is replaced by a far weaker `compatibility' assumption for uncorrelated quantum subsystems which, moreover, does not require the assignation of separate underlying properties to each subsystem (i.e, reductionism). Further, it is shown that an assumption of measurement independence may be dropped to obtain a related result having the same experimental significance (at the expense of a weaker conceptual significance). The latter is a remarkable feature of the PBR approach, given that Bell inequalities, steering inequalities and Kochen-Specker theorems all require an assumption of this type.
The aim of this paper is to present an analysis of the new theorem by Pusey, Barrett and Rudolph (PBR) concerning ontic and epistemic hidden variables in quantum mechanics [Nature Phys. 8, 476 (2012)]. This is a kind of review and defense of my previous critical analysis done in the context of Bohmian mechanics. This is also the occasion for me to review some of the fundamental aspects of Bohmian theory rarely discussed in the literature. The paper is submitted for the issue PBR theorem and Beyond of IJQF (International Journal of Quantum Foundations).
Pusey-Barrett-Rudolph theorem claims that ψ\psiψ-epistemic understanding of quantum mechanics is in trouble. Not considering whether the theorem only applies for realist understanding of quantum theory, this paper instead shows that the actual issue the theorem exposes is whether every quantum state should be interpreted as representing all sub-ensemble possibilities. For example, if ∣+⟩|+\rangle∣+⟩ was ``measured'' at time t=0t=0t=0 where ∣+⟩=(∣0⟩+∣1⟩)/2|+\rangle = (|0\rangle + |1 \rangle)/\sqrt{2}∣+⟩=(∣0⟩+∣1⟩)/2​, should we consider this quantum state as being solely ∣+⟩|+\rangle∣+⟩, or representing all possible sub-ensembles such as (+,0),(+,1)(+,0), (+,1)(+,0),(+,1)? This question suggests that PBR theorem does not rule out realist/non-realist ψ\psiψ-epistemic theory.
We review the Pusey-Barret-Rudolph (PBR) theorem\cite{PBR} and their setup, and arrive to the conclusion that the reality of a quantum state ψψψ is intrinsically attached to the measurement the system described by ψψψ has undergone. We show that a state that has not been measured can be regarded as pure information, while a state that has been measured has to be regarded as a physical property of a certain system, having a counterpart in reality. This demonstration implies that the statement of PBR's theorem changes in a meaningful way.