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arXiv:1812.08218 · Quantum

ψ -epistemic interpretations of quantum theory have a measurement problem

Joshua B. Ruebeck, Piers Lillystone, Joseph Emerson

Published Mar 16, 2020• 10 citations
arXivHTMLPDF

Abstract

ψ -epistemic interpretations of quantum theory maintain that quantum states only represent incomplete information about the physical states of the world. A major motivation for this view is the promise to provide a reasonable account of state update under measurement by asserting that it is simply a natural feature of updating incomplete statistical information. Here we demonstrate that all known ψ -epistemic ontological models of quantum theory in dimension d≥3 , including those designed to evade the conclusion of the PBR theorem, cannot represent state update correctly. Conversely, interpretations for which the wavefunction is real evade such restrictions despite remaining subject to long-standing criticism regarding physical discontinuity, indeterminism and the ambiguity of the Heisenberg cut. This revives the possibility of a no-go theorem with no additional assumptions, and demonstrates that what is usually thought of as a strength of epistemic interpretations may in fact be a weakness.

DOI
10.22331/q-2020-03-16-242

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ψ -epistemic interpretations of quantum theory maintain that quantum states only represent incomplete information about the physical states of the world. A major motivation for this view is the promise to provide a reasonable account of state update under measurement by asserting that it is simply a natural feature of updating incomplete statistical information. Here we demonstrate that all known ψ -epistemic ontological models of quantum theory in dimension d≥3 , including those designed to evade the conclusion of the PBR theorem, cannot represent state update correctly. Conversely, interpretations for which the wavefunction is real evade such restrictions despite remaining subject to long-standing criticism regarding physical discontinuity, indeterminism and the ambiguity of the Heisenberg cut. This revives the possibility of a no-go theorem with no additional assumptions, and demonstrates that what is usually thought of as a strength of epistemic interpretations may in fact be a weakness.
Since the famous debates of Einstein & Bohr, physicists have argued about the nature of the quantum state. Is it best thought of as describing the-way-things-are out there in the world, or merely as a description of our knowledge of such things? In more recent years, this has been termed the ψ-epistemic/ψ-ontic debate, and that distinction has been given a mathematical definition within the ontological models formalism. This formalism is a framework for describing a large class of interpretations of quantum mechanics. Here we show that consideration of sequential measurements, and the fact that the quantum state changes during measurements, has been a neglected topic in this area as it places nontrivial restrictions on the structure of ψ-epistemic ontological models. \n \nWe do this by finding a general restriction on the structure of ψ-epistemic models, although not one that is strong enough to rule them out categorically. We then apply this restriction to all of the known examples of ψ-epistemic ontological models and show that they can’t represent sequential measurements. We also present a new version of the ontological models formalism, based on hidden Markov models, which we develop briefly and describe how it may be useful for either proving a no-go theorem (i.e. ‘ψ-epistemic models can’t exist’) or for learning more about the structure of ψ-epistemic models and how to construct them.
Ψ-epistemic models of quantum mechanics imply that the quantum state does not correspond to physical reality, but instead reflects the observer's knowledge of the underlying quantum system. The epistemic view of the quantum state has the potential to shed light on several foundational problems of quantum theory and has attracted considerable attention in the literature. On the other hand, the Pusey-Barrett-Rudolph theorem demonstrated that broad classes of ψ-epistemic models must lead to predictions that deviate from those of quantum mechanics. Although the original theorem involved entangled joint measurements on composite systems, alternative no-go theorems involving measurements on single quantum systems were developed shortly thereafter. Experimental investigations of the deviations predicted by ψ-epistemic models from quantum mechanics are still ongoing. So far, such tests have been performed within the framework of non-relativistic quantum mechanics and predominantly rely on quantum information based measurement procedures. In this work, we show that ψ-epistemic models can give rise to deviations from standard quantum field-theoretic predictions through modifications of polarized scattering cross sections and decay widths. Our results do not require a relativistic formulation of ontological models or of the Harrigan-Spekkens criterion; the essential assumption is merely that measurements implemented through relativistic processes can still be represented within the ontological framework by well-defined response functions and probabilities. The present work constitutes a proof-of-principle study demonstrating that particle physics tests of the ontological status of the quantum state are possible and that ψ-epistemic models may exhibit experimentally distinguishable signatures in particle phenomenology.
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.
A novel no-go theorem is presented which sets a bound upon the extent to which 'Ψ-epistemic' interpretations of quantum theory are able to explain the overlap between non-orthogonal quantum states in terms of an experimenter's ignorance of an underlying state of reality. The theorem applies to any Hilbert space of dimension greater than two. In the limit of large Hilbert spaces, no more than half of the overlap between quantum states can be accounted for. Unlike other recent no-go theorems no additional assumptions, such as forms of locality, invasiveness, or non-contextuality, are required.
Abstract The ontological models framework distinguishes ψ-ontic from ψ-epistemic wave-functions. It is, in general, quite straightforward to categorize the wave-function of a certain quantum theory. Nevertheless, there has been a debate about the ontological status of the wave-function in the statistical interpretation of quantum mechanics: is it ψ-epistemic and incomplete or ψ-ontic and complete? I will argue that the wave-function in this interpretation is best regarded as ψ-ontic and incomplete.
Ontological models of quantum theory seek to realize quantum theory as a statistical theory over underlying degrees of freedom, whose measurement statistics are described by classical probability theory. Harrigan and Spekkens (2010) proposed a distinction between ontological models in which pure quantum states represent states of reality (ψ-ontic) or knowledge about reality (ψ-epistemic) depending on whether their associated probability distributions overlap, subsequently formalized into measure-theoretic form by Leifer (2014). In this thesis, I examine whether this ψ-ontic/epistemic distinction truly captures the intended difference between ontic and epistemic conceptions of pure states. I consider some mathematical alternatives relating to different notions of non-overlap between probability measures and compare them. I discuss the implications of these results for quantum ontology theorems – theorems that rule out ψ-epistemic readings of pure states under certain assumptions about the ontological model – such as the Pusey-Barrett-Rudolph Theorem (2012).