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Three-Spin Systems and the PBR Theorem

Zeynab Faroughi, Ali Ahanj, Samira Nazifkar, Kurosh Javidan

Published Jul 28, 2019• 0 citations
OpenAlex

Abstract

The fundamental nature of quantum wave function has been the subject of many discussions since the beginning of the quantum theory. It either corresponds to an element of reality $(\Psi-ontic)$ or it is a subjective state of knowledge about underlying reality $(\Psi-epistemic)$. Pusey, Barrett, and Rudolph (PBR) showed that epistemic interpretations of the quantum wave function are in contradiction with the predictions of quantum under some assumptions. In this paper, we introduce a laboratory protocol with triple quantum dot as a three-spin interaction system to study the PBR no-go theorem. By this experimental model, we show that the epistemic interpretation of the quantum state is in contradiction with quantum theory, based only on the assumption that measurement settings can be prepared freely and independent of each other.

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The fundamental nature of quantum wave function has been the subject of many discussions since the beginning of the quantum theory. It either corresponds to an element of reality (Ψ−ontic)(\Psi-ontic)(Ψ−ontic) or it is a subjective state of knowledge about underlying reality (Ψ−epistemic)(\Psi-epistemic)(Ψ−epistemic). Pusey, Barrett, and Rudolph (PBR) showed that epistemic interpretations of the quantum wave function are in contradiction with the predictions of quantum under some assumptions. In this paper, we introduce a laboratory protocol with triple quantum dot as a three-spin interaction system to study the PBR no-go theorem. By this experimental model, we show that the epistemic interpretation of the quantum state is in contradiction with quantum theory, based only on the assumption that measurement settings can be prepared freely and independent of each other.
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.
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.
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.
Protective measurements illustrate how Yakir Aharonov's fundamental insights into quantum theory yield new experimental paradigms that allow us to test quantum mechanics in ways that were not possible before. As for quantum theory itself, protective measurements demonstrate that a quantum state describes a single system, not only an ensemble of systems, and reveal a rich ontology in the quantum state of a single system. We discuss in what sense protective measurements anticipate the theorem of Pusey, Barrett, and Rudolph (PBR), stating that, if quantum predictions are correct, then two distinct quantum states cannot represent the same physical reality.