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On the reality of the quantum state

B.J.J. Bruggers

Published Aug 16, 2013• 0 citations
OpenAlex

Abstract

This paper explores the philosophical as well as the physical arguments made by Matthew Pusey, Jonathan Barrett and Terry Rudolph in their recently published article on the reality of the quantum state in order to attain a full understanding of the statements they make in their article. This is essential because not even all respondents to the article agree on how to interpret the article. In their article Pusey, Barrett and Rudolph present a no-go theorem; they show that a particular situation is, according to quantum theory, not physically possible if one were to be psi-epistemic about it. They argue that for this particular situation, or thought-experiment, the psi-epistemic interpretation makes predictions that are inconsistent with those predictions made by quantum theory itself.

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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 would imply many of the known no-go theorems, such as Bell's Theorem and the need for an exponentially large ontic state space; Provides a comprehensive presentation of the Pusey–Barrett–Rudolph Theorem itself, along with subsequent improvements and criticisms of its assumptions; Reviews two other arguments for the reality of the quantum state: the first due to Hardy and the second due to Colbeck and Renner, and explains why their assumptions are less compelling than those of the Pusey–Barrett–Rudolph Theorem; Reviews subsequent work aimed at ruling out stronger notions of what it means for the quantum state to be epistemic and points out open questions in this area. The overall aim is not only to provide the background needed for the novice in this area to understand the current status, but also to discuss often overlooked subtleties that should be of interest to the experts. Quanta 2014; 3: 67–155.

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Comment to 'On the reality of the quantum state'

Marcoen J. T. F. Cabbolet

In Nature Phys. 8:475-478 (2012), Pusey, Barrett, and Rudolph have claimed that ψ-epistemic quantum mechanics (QM) is inconsistent with predictions of standard QM. Here we show that Pusey et al. err in the beginning of their argument by making an assumption that violates the Projection Postulate.

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This paper explores the philosophical as well as the physical arguments made by Matthew Pusey, Jonathan Barrett and Terry Rudolph in their recently published article on the reality of the quantum state in order to attain a full understanding of the statements they make in their article. This is essential because not even all respondents to the article agree on how to interpret the article. In their article Pusey, Barrett and Rudolph present a no-go theorem; they show that a particular situation is, according to quantum theory, not physically possible if one were to be psi-epistemic about it. They argue that for this particular situation, or thought-experiment, the psi-epistemic interpretation makes predictions that are inconsistent with those predictions made by quantum theory itself.
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 would imply many of the known no-go theorems, such as Bell's Theorem and the need for an exponentially large ontic state space; Provides a comprehensive presentation of the Pusey–Barrett–Rudolph Theorem itself, along with subsequent improvements and criticisms of its assumptions; Reviews two other arguments for the reality of the quantum state: the first due to Hardy and the second due to Colbeck and Renner, and explains why their assumptions are less compelling than those of the Pusey–Barrett–Rudolph Theorem; Reviews subsequent work aimed at ruling out stronger notions of what it means for the quantum state to be epistemic and points out open questions in this area. The overall aim is not only to provide the background needed for the novice in this area to understand the current status, but also to discuss often overlooked subtleties that should be of interest to the experts. Quanta 2014; 3: 67–155.
The Pusey-Barrett-Rudolph (PBR) no-go theorem provides an argument for the reality of the quantum state by ruling out $\ensuremath{\psi}$-epistemic ontological theories, in which the quantum state is of a statistical nature. It applies under an assumption of preparation independence, the validity of which has been subject to debate. We propose two plausible and less restrictive alternatives: a weaker notion allowing for classical correlations, and an even weaker, physically motivated notion of independence, which merely prohibits the possibility of superluminal causal influences in the preparation process. The latter is a minimal requirement for enabling a reasonable treatment of subsystems in any theory. It is demonstrated by means of an explicit $\ensuremath{\psi}$-epistemic ontological model that the argument of PBR becomes invalid under the alternative notions of independence. As an intermediate step, we recover a result which is valid in the presence of classical correlations. Finally, we obtain a theorem which holds under the minimal requirement, approximating the result of PBR. For this, we consider experiments involving randomly sampled preparations and derive bounds on the degree of $\ensuremath{\psi}$ epistemicity that is consistent with the quantum-mechanical predictions. The approximation is exact in the limit as the sample space of preparations becomes infinite.
The quantum state ψ is a mathematical object used to determine the probabilities of different outcomes when measuring a physical system. Its fundamental nature has been the subject of discussions since the inception of quantum theory. Is it ontic, that is, does it correspond to a real property of the physical system? Or is it epistemic, that is, does it merely represent our knowledge about the system? Assuming a natural continuity assumption and a weak separability assumption, we show here that epistemic interpretations of the quantum state are in contradiction with quantum theory. Our argument is different from the recent proof of Pusey, Barrett, and Rudolph and it already yields a nontrivial constraint on ψ-epistemic models using a single copy of the system in question.
I argue for a realist interpretation of the quantum state. I begin by reviewing and critically evaluating two arguments for an antirealist interpretation of the quantum state, the first derived from the so-called ‘measurement problem’, and the second from the concept of local causality. I argue that existing antirealist interpretations do not solve the measurement problem. Furthermore, I argue that it is possible to construct a local, realist interpretation of quantum mechanics, using methods borrowed from quantum field theory and based on John S. Bell’s concept of ‘local beables’.\nIf the quantum state is interpreted subjectively, then the probabilities it associates with experimental outcomes are themselves subjective. I address the prospects for developing a subjective Bayesian interpretation of quantum mechanical probabilities based on the Quantum de Finetti Representation Theorem. Epistemic interpretations of the quantum state can be divided into those that are epistemic with respect to underlying ontic states, and those that are epistemic with respect to measurement outcomes. The Pusey Barrett and Rudolph (PBR) theorem places serious constraints on the former family of interpretations. I identify an important explanatory gap in the latter sort of interpretation. In particular, if the quantum state is a subjective representation of beliefs about future experimental outcomes, then it is not clear why those experimenters who use quantum mechanics should be better able to negotiate the world than those who do not.\nI then turn to the task of articulating a positive argument for the thesis of quantum state realism. I begin by articulating a minimal set of conditions that any realist interpretation must meet. One assumption built into the PBR result is that systems prepared in a given quantum state have a well-defined set of physical properties, which may be completely or incompletely described by the quantum state. Antirealist interpretations that reject this assumption are therefore compatible with the PBR result. A compelling case for quantum state realism must therefore be made on more general grounds. I consider two concrete examples of phenomena described by quantum mechanics that strongly suggest that the quantum state is genuinely representational in character.
The Pusey--Barrett--Rudolph (PBR) theorem is commonly taken to establish that a pure quantum state represents a physical property of the system to which it is assigned, rather than merely encoding knowledge. In this work, I distinguish between state-first and dynamics-first physical theories, and argue that this reading presupposes the former. These two types of theories support different approaches to causal explanation, and one of PBR's stated assumptions depends on the state-first approach. Using a recent interpretation of quantum theory as a concrete example, I show how a dynamics-first theory can explain the PBR correlations while maintaining a broadly epistemic reading of quantum states. I conclude that the PBR theorem supports a dilemma: either the quantum state is part of reality, or reality is not fundamentally built out of states.