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arXiv:1203.2475

Can quantum mechanics be considered as statistical? an analysis of the PBR theorem

Aurélien Drezet

Published Mar 12, 2012• 5 citations
arXivHTMLPDF

Abstract

The answer to this question is `yes it can!' as we will see in this manuscript. More, precisely after a discussion of M. F. Pusey, J. Barrett and T. Rudolph (PBR) result (arXiv:1111.3328) we will show that contrarily to the PBR claim the epistemic approach is in general not disproved by their `no-go' theorem.

DOI
10.48550/arxiv.1203.2475

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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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The answer to this question is yes it can!' as we will see in this manuscript. More, precisely after a discussion of M. F. Pusey, J. Barrett and T. Rudolph (PBR) result (arXiv:1111.3328) we will show that contrarily to the PBR claim the epistemic approach is in general not disproved by their no-go' theorem.
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.
"In the past couple of months, the quantum foundations world has been abuzz about a new preprint entitled "The Quantum State Cannot be Interpreted Statistically" by Matt Pusey, Jon Barrett and Terry Rudolph (henceforth known as PBR). Since I wrote a blog post explaining the result, I have been inundated with more correspondence from scientists and more requests for comment from science journalists than at any other point in my career. Reaction to the result amongst quantum researchers has been mixed, with many people reacting negatively to the title, which can be misinterpreted as an attack on the Born rule. Others have managed to read past the title, but are still unsure whether to credit the result with any fundamental significance. In this article, I would like to explain why I think that the PBR result is the most significant constraint on hidden variable theories that has been proved to date. It provides a simple proof of many other known theorems, and it supercharges the EPR argument, converting it into a rigorous proof of nonlocality that has the same status as Bell's theorem. Before getting to this though, we need to understand the PBR result itself."
In a recent paper (arXiv:1111.3328), Pusey, Barrett and Rudolph claim to prove that statistical interpretations of quantum mechanics do not work. In fact, their proof assumes that all statistical interpretations must be based on hidden variable realism. Effectively, the authors demand from the start that reality must be decided by mathematics, and not by measurements. If this unjustified assumption is dropped, the quantum formalism has a natural statistical interpretation that fully explains the paradox presented by the authors. It is therefore possible to conclude that the paradox actually supports the statistical interpretation, demonstrating once more that quantum mechanics should not be explained by measurement independent realities that are never observed and therefore lie beyond the reach of empirical tests.
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.