Is the quantum state real? An extended review of $ψ$-ontology theorems (1409.1570v2)

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 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.

• The paper presents a comprehensive review demonstrating that, under specific assumptions, the quantum state must be recognized as an ontic element of reality.
• It critically analyzes the PBR, Hardy’s, and Colbeck-Renner theorems by examining their methodological foundations such as preparation independence and ontic indifference.
• The discussion highlights key challenges and implications for quantum mechanics, influencing perspectives on nonlocality, completeness, and quantum information theory.

Overview of Psi-Ontology Theorems in Quantum Mechanics

The subject of whether the quantum state, or wavefunction, is a real physical object or merely a mathematical tool has generated substantial debate in the field of quantum foundations. Matthew Saul Leifer's comprehensive review of $\psi$-ontology theorems rigorously examines whether the quantum state must be considered ontic—representing objective reality—or epistemic—representing knowledge about the system. This essay explores the primary motivations, assumptions, criticisms, and implications of the $\psi$-ontology results, with special attention to three main theorems: the Pusey-Barrett-Rudolph (PBR) Theorem, Hardy's Theorem, and the Colbeck-Renner Theorem.

Psi-Ontology vs. Psi-Epistemic Models

At the heart of the debate is the ontic/epistemic distinction in quantum state interpretation. A $\psi$-ontic model treats the quantum state as an objective part of reality, uniquely associated with the ontic conditions of the system. Conversely, in a $\psi$-epistemic model, the quantum state is a state of knowledge or belief about an underlying ontic state. This ontological question impacts how we understand the intrinsic probabilistic nature of quantum mechanics and challenges the traditional view instantiated by interpretations such as the Copenhagen interpretation.

The Pusey-Barrett-Rudolph Theorem

The PBR Theorem argues that for a broad class of realist approaches to quantum mechanics, the quantum state must be ontic. The PBR Theorem relies on a technical assumption known as the Preparation Independence Postulate (PIP), which asserts that subsystems prepared independently and then brought together ought to have ontic states that form a Cartesian product. The assumptions underlying this theorem have been subject to extensive scrutiny and criticism, particularly regarding the PIP's necessity and implications for locality and non-locality. Nevertheless, the theorem has garnered significant attention for challenging the psi-epistemic perspective.

Hardy's Theorem

Hardy's approach to $\psi$-ontology involves a different assumption termed ontic indifference. This asserts that if a quantum state remains invariant under some unitary transformations, this invariance should manifest at the ontic level by leaving the ontic states unchanged. Hardy's Theorem manages to relate interference—a phenomenon often cited in arguments for ontology—to the need for a psi-ontic interpretation. However, the assumption of ontic indifference is contentious since it can vary widely between theories, particularly psi-epistemic models, which often do not recognize ontic indifference.

The Colbeck-Renner Theorem

The Colbeck-Renner Theorem extends the debate to consider whether more informative predictions can be generated from ontic state information than by using the quantum state alone. The theorem is grounded in a notion of parameter independence, which constrains the dependence of measurement outcomes on the distant choice of settings, similar to Bell's locality framework but less restrictive. It takes advantage of chained Bell measurements to demonstrate that, under parameter independence, a psi-ontic interpretation is necessary. This theorem underscores the tension between quantum mechanics and our classical intuitions of locality and causality.

Criticisms and Challenges

Each theorem faces unique challenges, notably concerning their assumptions. Critics of the PBR theorem argue that the Preparation Independence Postulate is overly restrictive, with some suggesting that it fails to account for potential subquantum correlations. Hardy's notion of ontic indifference seems unnatural within psi-epistemic frameworks, which typically do not justify such uniformity at the ontic level. The Colbeck-Renner Theorem, drawing upon parameter independence, struggles with balancing nonlocal explanations akin to those required in responses to Bell's Theorem.

Implications and Future Directions

The implications of these theorems touch on several pivotal issues in quantum mechanics, notably the nature of quantum nonlocality, the completeness of quantum mechanics, and foundational topics such as the interpretation of probabilities in quantum theory. Consequences like Bell's Theorem, preparation contextuality, and excess baggage are intricately connected to the conclusions drawn from these $\psi$-ontology theorems.

The ongoing development of quantum information theory is particularly likely to be influenced by further exploration of these foundational questions, with potential impacts on quantum computing paradigms, quantum cryptography, and understanding of entanglement.

In summary, although $\psi$-ontology theorems create a compelling argument for the realism of the quantum state, they also vividly illustrate the challenges of aligning quantum mechanics with classical intuitions of reality and locality. The field continues to evolve, driven by both theoretical innovations and experimental advances aimed at testing these profound philosophical questions.