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arXiv:1806.05323

Quantum theory is not only about information

Laura Felline

Published Jun 13, 2018• 2 citations
arXivHTMLPDF

Abstract

In his recent book Bananaworld. Quantum mechanics for primates, Jeff Bub revives and provides a mature version of his influential information theoretic interpretation of Quantum Theory (QT). In this paper, I test Bub s conjecture that QT should be interpreted as a theory about information, by examining whether his information theoretic interpretation has the resources to explain (or explain away) quantum conundrums. The discussion of Bub s theses will also serve to investigate, more in general, whether other approaches succeed in defending the claim that QT is about quantum information. First of all, I argue that Bub s interpretation of QT as a principle theory fails to fully explain quantum nonlocality. Secondly, I argue that a constructive interpretation, where the quantum state is interpreted ontically as information, also fails at providing a full explanation of quantum correlations. Finally, while epistemic interpretations might succeed in this respect, I argue that such a success comes at the price of rejecting some in between the most basic scientific standards of physical theories.

DOI
10.48550/arxiv.1806.05323

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In his recent book Bananaworld. Quantum mechanics for primates, Jeff Bub revives and provides a mature version of his influential information theoretic interpretation of Quantum Theory (QT). In this paper, I test Bub s conjecture that QT should be interpreted as a theory about information, by examining whether his information theoretic interpretation has the resources to explain (or explain away) quantum conundrums. The discussion of Bub s theses will also serve to investigate, more in general, whether other approaches succeed in defending the claim that QT is about quantum information. First of all, I argue that Bub s interpretation of QT as a principle theory fails to fully explain quantum nonlocality. Secondly, I argue that a constructive interpretation, where the quantum state is interpreted ontically as information, also fails at providing a full explanation of quantum correlations. Finally, while epistemic interpretations might succeed in this respect, I argue that such a success comes at the price of rejecting some in between the most basic scientific standards of physical theories.
The principle aim of this dissertation is to investigate the philosophical application of quantum information theory to interpretational issues regarding the theory of quantum mechanics. Recently, quantum information theory has emerged as a potential source for such an interpretation. The main question with which this dissertation will be concerned is whether or not an information-theoretic interpretation can serve as a conceptually acceptable interpretation of quantum mechanics. It will be argued that some of the more obvious approaches - that quantum information theory shows us that ultimately the world is made of information, and quantum Bayesianism - fail as philosophical interpretations of quantum mechanics. However, the information-theoretic approach of Clifton, Bub, and Halvorson introduces Einstein's distinction between principle theories and constructive theories, arguing that quantum mechanics is best understood as an information-theoretic principle theory. While I argue that this particular approach fails, it does offer a viable new philosophical role for information theory. Specifically, an investigation of interpretationally successful principle theories such as Newtonian mechanics, special relativity, and general relativity, shows that the particular principles employed are necessary as constitutive elements of a framework which partially defines the basic explanatory concepts of space, time, and motion. Without such constitutive principles as preconditions for empirical meaning, scientific progress is hampered. It is argued that the philosophical issues in quantum mechanics stem from an analogous conceptual crisis. On the basis of this comparison, the best strategy for resolving these problems is to apply a similar sort of conceptual analysis to quantum mechanics so as to provide an appropriate set of constitutive principles clarifying the conceptual issues at stake. It is further argued that quantum information theory is ideally placed as a novel conceptual framework from which to conduct this analysis.
The aim of this paper is to explore the ways in which Axiomatic Reconstructions of Quantum Theory in terms of Information-Theoretic principles (ARQITs) can contribute to explaining and understanding quantum phenomena, as well as to study their explanatory limitations. This is achieved in part by offering an account of the kind of explanation that axiomatic reconstructions of Quantum Theory provide, and re-evaluating the epistemic status of the program in light of this explanation. As illustrative case studies, I take Clifton's, Bub's and Halvorson's characterization theorem and Popescu's and Rohrlich's toy models, and their explanatory contribution with respect to quantum nonlocality. On the one hand, I argue that ARQITs can aspire to provide genuine explanations of (some aspects of) quantum nonlocality. On the other hand, I argue that such explanations cannot rule out a mechanical quantum theory.
We give a condensed and accessible summary of a recent derivation of quantum theory from information-theoretic principles, and use it to study the consequences of this and other reconstructions for our conceptual understanding of the quantum world. Since these principles are to a large extent expressed in computational terminology, we argue that the hypothesis of "physics as computation", if suitably interpreted, attains surprising explanatory power. Similarly as Jeffrey Bub and others, we conclude that quantum theory should be understood as a "principle theory of information", and we regard this view as a partial interpretation of quantum theory. We outline three options for completion into a full-fledged interpretation of quantum theory, but argue that, despite their interpretational agnosticism, the principled reconstructions pose a challenge for existing psi-ontic interpretations. We also argue that continuous reversible time evolution can be understood as a characteristic property of quantum theory, offering a possible answer to Chris Fuchs' search for a "glimpse of quantum reality".
A remarkable theorem by Clifton, Bub and Halvorson (2003) (CBH) characterizes quantum theory in terms of information--theoretic principles. According to Bub (2004, 2005) the philosophical significance of the theorem is that quantum theory should be regarded as a ``principle'' theory about (quantum) information rather than a ``constructive'' theory about the dynamics of quantum systems. Here we criticize Bub's principle approach arguing that if the mathematical formalism of quantum mechanics remains intact then there is no escape route from solving the measurement problem by constructive theories. We further propose a (Wigner--type) thought experiment that we argue demonstrates that quantum mechanics on the information--theoretic approach is incomplete.
Some approaches which seek to make progress with the conceptual troubles of quantum theory using information-theoretic ideas are investigated. These include Zeilinger’s Foundational Principle and the information-theoretic characterization theorem of Clifton, Bub and Halvorson. It is shown that Zeilinger’s Foundational Principle does not provide a foundational principle for quantum mechanics and fails to underwrite explanations of the randomness of quantum measurement and the existence of entanglement. The Clifton- Bub-Halvorson theorem is more positively assessed: here an axiomatisation of quantum mechanics has been achieved. However some questions are raised concerning the C ∗-algebraic starting point of the theorem, which seems not a sufficiently neutral theoretical framework for the axiomatic project. Moreover, it is argued that rather than the Clifton-Bub-Halvorson result motivating an information-theoretic approach (principle theory approach) to understanding the quantum world which obviates our traditional concerns, such an approach simply fails to engage with the crucial interpretational issues.
The interpretative principle proposed by Bub in 1211.3062v1 [quant-ph] is justified only for all practical purposes (Bell's "FAPP trap"). An alternative interpretative principle is proposed. It brings to light those features of the quantum world because of which the fundamental theoretical framework of physics is a "mere" probability calculus, and it amply justifies Bohr's insistence that quantum-mechanical observables cannot be defined without reference to the experimental conditions in which they are measured. It implies that the spatial distinctions we make cannot be intrinsic to space, that regions "of space" must be realized by macroscopic objects, that the spatiotemporal differentiation of the physical world is incomplete, that the positions of macroscopic objects (suitably defined) are definite in a nonclassical sense, and that unconditional factuality can be consistently attributed to them.