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La natura dello stato quantistico: realtà o informazione.

Andrea Sangiovanni

Published Jul 1, 2016• 0 citations
OpenAlex

Abstract

After an analysis of the theories of quantum mechanics based upon ontological models, we have examined the recent PBR theorem, which rules out the possibility that informational ontological models may be compatible with quantum mechanics itself. Finally, consequences of the PBR theorem have been highlighted.

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In questa tesi sostengo che l’interpretazione modale della Meccanica Quantistica, almeno nella versione di van Fraassen del 1991 ed in quella di Kochen-Dieks, non soddisfa le ipotesi del teorema PBR. Tale teorema dimostra che una certa classe di interpretazioni (specificamente i modelli ontologici ψ-epistemici e ψ-indipendenti) porta a prevedere risultati sperimentali in contrasto con quelli previsti dalla Meccanica Quantistica teorizzata da von Neumann, e dunque sia da rigettare. In particolare dimostro, in contrasto con quanto suggerito da Leifer in un articolo apparso sulla rivista Quanta nel 2014, che l’interpretazione modale e un modello ontologico ψ-epistemico. Tuttavia esso e anche ψ-dipendente, dunque il teorema PBR non invalida questa interpretazione. In riferimento al titolo, l’interpretazione modale prevede che lo stato quantico sia in parte reale ed in parte epistemico, e nella tesi esporro in che senso. Il totale realismo sulla funzione d’onda prescritto dal teorema PBR e invece incompatibile con una sua interpretazione modale. In this thesis I prove that modal interpretation of Quantum Mechanics, at least in the van Frassen’s version and in Kochen-Dieks’ one, doesn’t satisfy the hypothesis of PBR theorem. This theorem demonstrates that a certain class of interpretations (namely onthological ψ-epistemic ψ-independent models) predict experimental results in contrast with the ones predicted by Quantum Mechanics as theorized by von Neumann, and so is to be rejected. In particular I demonstrate, in contrast with what Leifer suggests in an article published on the review Quanta in 2014, that modal interpretation is a ψ-epistemic model. I show as well that it is also ψ-dependent, so PBR theorem doesn’t invalidate this interpretation. Referring to the title, modal interpretation says that quantum state is partly real and partly epistemic, and in the thesis I will explain in which sense. The total realism on the wavefunction prescribed by PBR theorem is on the contrary incompatible with a modal interpretation of it.

•Nov 26, 2018•0 citations
In this paper, we show that Quantum Mechanics does not admit ontological models, in the sense that the quantum state of a system cannot correspond to a set of physical states representing the independent reality of the system. We show, via two thought experiments based on the Wigner's friend scenario, that if the ontic state of physical systems in the lab is the same for Wigner and for his friend, one of the following will be violated: PBR theorem, Quantum-theoretic predictions, and the "No-superdeterminism" assumption.
Abstract According to Relational Quantum Mechanics (RQM) the wave function ψ\psiψ ψ is considered neither a concrete physical item evolving in spacetime, nor an object representing the absolute state of a certain quantum system. In this interpretative framework, ψ\psiψ ψ is defined as a computational device encoding observers’ information; hence, RQM offers a somewhat epistemic view of the wave function. This perspective seems to be at odds with the PBR theorem, a formal result excluding that wave functions represent knowledge of an underlying reality described by some ontic state. In this paper we argue that RQM is not affected by the conclusions of PBR’s argument; consequently, the alleged inconsistency can be dissolved. To do that, we will thoroughly discuss the very foundations of the PBR theorem, i.e. Harrigan and Spekkens’ categorization of ontological models, showing that their implicit assumptions about the nature of the ontic state are incompatible with the main tenets of RQM. Then, we will ask whether it is possible to derive a relational PBR-type result, answering in the negative. This conclusion shows some limitations of this theorem not yet discussed in the literature.
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.
In questa tesi sostengo che l’interpretazione modale della Meccanica Quantistica, almeno nella versione di van Fraassen del 1991 ed in quella di Kochen-Dieks, non soddisfa le ipotesi del teorema PBR. Tale teorema dimostra che una certa classe di interpretazioni (specificamente i modelli ontologici ψ-epistemici e ψ-indipendenti) porta a prevedere risultati sperimentali in contrasto con quelli previsti dalla Meccanica Quantistica teorizzata da von Neumann, e dunque sia da rigettare. In particolare dimostro, in contrasto con quanto suggerito da Leifer in un articolo apparso sulla rivista Quanta nel 2014, che l’interpretazione modale e un modello ontologico ψ-epistemico. Tuttavia esso e anche ψ-dipendente, dunque il teorema PBR non invalida questa interpretazione. In riferimento al titolo, l’interpretazione modale prevede che lo stato quantico sia in parte reale ed in parte epistemico, e nella tesi esporro in che senso. Il totale realismo sulla funzione d’onda prescritto dal teorema PBR e invece incompatibile con una sua interpretazione modale. In this thesis I prove that modal interpretation of Quantum Mechanics, at least in the van Frassen’s version and in Kochen-Dieks’ one, doesn’t satisfy the hypothesis of PBR theorem. This theorem demonstrates that a certain class of interpretations (namely onthological ψ-epistemic ψ-independent models) predict experimental results in contrast with the ones predicted by Quantum Mechanics as theorized by von Neumann, and so is to be rejected. In particular I demonstrate, in contrast with what Leifer suggests in an article published on the review Quanta in 2014, that modal interpretation is a ψ-epistemic model. I show as well that it is also ψ-dependent, so PBR theorem doesn’t invalidate this interpretation. Referring to the title, modal interpretation says that quantum state is partly real and partly epistemic, and in the thesis I will explain in which sense. The total realism on the wavefunction prescribed by PBR theorem is on the contrary incompatible with a modal interpretation of it.