Quantum Theory as a Principle Theory: Insights from an Information-Theoretic Reconstruction

Abstract

We give a condensed and accessible summary of a recent derivation of quantum theory from informationtheoretic 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 ψ-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". 1 The citations listed above are not to the originators of the interpretations; rather, they provide general overviews of each interpretation as each currently stands. 2 Feintzeig [Fei14] has questioned the applicability of the ontological models framework to Bohmian mechanics. For the purpose of our argumentation, however, it is sufficient to consider a qualitative distinction between ψ-epistemic and ψ-ontic theories, since none of our arguments rely on the formal mathematical definition of these notions in terms of the ontological models framework. arXiv:1707.05602v1 [quant-ph] 18 Jul 2017A key figure in merging quantum information theory with foundational work in quantum mechanics was John A. Wheeler [Whe83], whose "It from Bit" doctrine-that the fundamental stuff of the universe is information-led to attempts to provide a coherent ontological story for quantum theory in information-theoretic terms. Clifton, Bub, and Halvorson (CBH) [CBH03] appeared to have gone a long way towards this goal in their 2003 paper. They assume a background theory space characterized by C * -algebras, which are general enough to include both classical and quantum theories, and derive the algebraic structure of standard quantum theory from information-theoretic postulates. In response to Wheeler, CBH "are suggesting that quantum theory be viewed. . . as a theory about the possibilities and impossibilities of information transfer" (p. 1563).One of the major drawbacks of the CBH approach (later acknowledged by one of the authors [Bub16]) is that it relies on a C *algebraic framework for theories. 3 Though the framework is general enough to include both classical and quantum theories, 4 its structure is rather restrictive, and builds in many assumptions that are crucial to quantum theories. Given the CBH reconstruction of quantum theory, the natural question to ask is, "Why C * -algebras for physical theories, rather than something else?"Independently f...

Understanding quantum mechanics: a review and synthesis in precise language

“…It has been suggested, subject to assumptions, that only segregated model (ontic) theories reproduce the predictions of quantum mechanics [215]. Despite this, many still view the quantum mechanical state as wholly or partly epistemic [213,216,217]. Their view is tenable given the clear scope to reject or challenge one or more of the explicit or implicit assumptions [ [219][220][221][222].…”

“…The question of how an information-theoretic based approach can be linked to independent reality has also prompted some other responses [216].…”

“…-'Properties' in quantum mechanics can be viewed as descriptions of how one system influences others, rather than attributes possessed by the system [314,505]. -An information-based principle theory may reflect an underlying constructive theory [216], of the type outlined in Sect. 6.7 below.…”

Agent Inaccessibility as a Fundamental Principle in Quantum Mechanics: Objective Unpredictability and Formal Uncomputability

“…Notably, contextuality might represent the “non-information-theoretic kernel” of quantum theory, Koberinski and Müller [ 43 ] have suggested recently, and that therefore contextuality could be a genuine physical (ontological) feature of a possible quantum reality. With respect to contextuality as a “genuine physical feature”, the investigators cited Fuchs [ 44 ] who had also expressed the similar hope earlier that the “…distillate that remains—a piece of quantum theory with no information-theoretic significance—will be our first unadorned glimpse of ‘quantum reality’.” Related to that suggestion, the following idea is here pursued also: what Koberinski and Müller [ 43 ] have referred to as the “non-information-theoretic kernel” of quantum theory may refer directly to the uncomputable ontological features that are the topic of the present article (compare Section 6 ).…”

“…Very recently, the potential power of the approach that combines the notion of universal computation with unconventional ontological propositions has also been noted, for example, by Koberinski and Müller [ 43 ]. They considered the kind of information-theoretic properties of quantum theory “…which are directly linked to the possibility of having a universal computing machine, like the quantum Turing machine”, which is “…in principle able to simulate the time evolution of any physical system”.…”