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.
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.
This paper is a commentary on the foundational significance of the Clifton-Bub-Halvorson theorem characterizing quantum theory in terms of three information-theoretic constraints (Foundations of Physics 33, 1561-1591 (2003); quant-ph/0211089). I argue that: (1) a quantum theory is best understood as a theory about the possibilities and impossibilities of information transfer, as opposed to a theory about the mechanics of nonclassical waves or particles, (2) given the information-theoretic constraints, any mechanical theory of quantum phenomena that includes an account of the measuring instruments that reveal these phenomena must be empirically equivalent to a quantum theory, and (3) assuming the information-theoretic constraints are in fact satisfied in our world, no mechanical theory of quantum phenomena that includes an account of measurement interactions can be acceptable, and the appropriate aim of physics at the fundamental level then becomes the representation and manipulation of information.
Introduction Many philosophers and physicists have expressed great hope that quantum information theory will help us understand the nature of the quantum world. The general problem is that there is no widespread agreement on what quantum information is. Hence, such pronouncements regarding quantum information theory as the savior of the philosophy of physics are hard to evaluate. Much work has been done producing and evaluating concepts of information. In I have defended and articulated the Schumacher concept of quantum information. Roughly speaking, quantum information is construed as the statistical behavior associated with the measurement of a quantum system. Hence it is a coarse-grained operational description of quantum systems, with no recourse to the fundamental ontological features of quantum systems responsible for such behavior. From this perspective, construing quantum mechanics as a theory of quantum information departs from the traditional interpretive endeavors of philosophers and physicists. The question is whether there is any motivation for taking such a view. The theorem of Clifton, Bub, and Halvorson (CBH) provides just such a motivation. The theorem guarantees that, if a theory T satisfies certain conditions, there will exist an empirically equivalent C *-algebraic theory that has a concrete representation in Hilbert space, which it is notoriously difficult to interpret as a constructive or mechanical theory. In such a case, any underlying ontologies philosophers develop that are compatible with T will be undermined by the C*-algebraic equivalent. Bub suggests in light of this in-principle uncertainty regarding ontology that we re-conceive of quantum mechanics as a theory about quantum information.
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.
This paper is a commentary on the foundational significance of the Clifton-Bub-Halvorson theorem characterizing quantum theory in terms of three information-theoretic constraints (Foundations of Physics 33, 1561-1591 (2003); quant-ph/0211089). I argue that: (1) a quantum theory is best understood as a theory about the possibilities and impossibilities of information transfer, as opposed to a theory about the mechanics of nonclassical waves or particles, (2) given the information-theoretic constraints, any mechanical theory of quantum phenomena that includes an account of the measuring instruments that reveal these phenomena must be empirically equivalent to a quantum theory, and (3) assuming the information-theoretic constraints are in fact satisfied in our world, no mechanical theory of quantum phenomena that includes an account of measurement interactions can be acceptable, and the appropriate aim of physics at the fundamental level then becomes the representation and manipulation of information.
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.
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.