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.
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).
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 main question under investigation in this thesis was the reality of the quantum state. We approached this problem by studying a recent no-go result by Pusey, Barrett and Rudolph, namely the PBR theorem. In Section 1 we provided a short introduction to quantum theory. A few relevant examples were covered, namely decompositions of quantum states, impossibility of the ignorance interpretation and the distinguishability of pure quantum states. Section 2 developed measure theoretic tools needed in the framework of ontological models. The Radon-Nikodym theorem was proven in order to justify the use of an alternative expression of the variational distance of probability measures. In Section 3 we developed a general framework for ontological models. In short, the ontological models framework can be considered the most general framework currently available for hidden variable theories and no-go results. We used the measure theoretic tools of Section 2 to make the formalism rigorous. Original research included in Section 3 was the characterization of a property called antidistinguishability for qubit states. A necessary and sufficient condition for antidistinguishability was given. It was then proven that any set of pure qubit states that is not antidistinguishable can be made antidistinguishable by adding a single carefully chosen state into the set. In the end of Section 3, some original observations were presented. Namely, a specific connection with contextuality was proven for sometimes ψ-ontic and never ψ-ontic ontological models. However, it was then noted that these observations were not enough to exclude never ψ-ontic ontological models, a feat that would have provided a new no-go theorem on its own. Contextuality in the ontological models framework was studied in Section 4. The main results were establishing preparation contextuality from the failure of maximal ψ-epistemicity and a proof of Bell's theorem based on preparation contextuality established this way. We concluded that ψ-ontic models cannot be Bell local based on these results. Finally in Section 5 the implications of ψ-ontology were discussed. By careful analysis of the results, it was noted that accepting the reality of the quantum state exposes explanatory gaps in the formalism. Possible solutions to the challenges introduced by these explanatory gaps were discussed through interpretations of quantum mechanics and the so-called measurement problem.
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.
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.
Abstract Harrigan and Spekkens (Found Phys 40:125–157, 2010) provided a categorization of quantum ontological models classifying them as
ψ ψ -ontic or
ψ ψ -epistemic if the quantum state
ψ ψ describes respectively either a physical reality or mere observers’ knowledge. Moreover, they claimed that Einstein—who was a supporter of the statistical interpretation of quantum mechanics—endorsed an epistemic view of
ψ. ψ. In this essay we critically assess such a classification and some of its consequences by proposing a twofold argumentation. Firstly, we show that Harrigan and Spekkens’ categorization implicitly assumes that a complete description of a quantum system (its ontic state,
λ λ ) only concernssingle,individualsystems instantiatingabsolute,intrinsicproperties. Secondly, we argue that such assumptions conflict with some current interpretations of quantum mechanics, which employ different ontic states as a complete description of quantum systems. In particular, we will show that, since in the statistical interpretation ontic states describe ensembles rather than individuals, such a view cannot be considered
ψ ψ -epistemic. As a consequence, the authors misinterpreted Einstein’s view concerning the nature of the quantum state. Next, we will focus onrelational quantum mechanicsandperspectival quantum mechanics, which in virtue of their relational and perspectival metaphysics employ ontic states
λ λ dealing with relational properties. We conclude that Harrigan and Spekkens’ categorization is too narrow and entails an inadequate classification of the mentioned interpretations of quantum theory. Hence, any satisfactory classification of quantum ontological models ought to take into account the variations of
λ λ across different interpretations of quantum mechanics.