Quantum Information Theory and the Foundations of Quantum Mechanics Oxford Philosophical Monographs

Quantum Information Theory and the Foundations of Quantum Mechanics is a conceptual analysis of one of the most prominent and exciting new areas of physics, providing the first full-length philosophical treatment of quantum information theory and the questions it raises for our understanding of the quantum world. Beginning from a careful, revisionary analysis of the concepts of information in the everyday and classical information-theory settings, Christopher G. Timpson argues for an ontologically deflationary account of the nature of quantum information. Against what many have supposed, quantum information can be clearly defined (it is not a primitive or vague notion) but it is not part of the material contents of the world. Timpson's account sheds light on the nature of nonlocality and information flow in the presence of entanglement and, in particular, dissolves puzzles surrounding the remarkable process of quantum teleportation. In addition it permits a clear view of what the ontological and methodological lessons provided by quantum information theory are; lessons which bear on the gripping question of what role a concept like information has to play in fundamental physics. Topics discussed include the slogan 'Information is Physical', the prospects for an informational immaterialism (the view that information rather than matter might fundamentally constitute the world), and the status of the Church-Turing hypothesis in light of quantum computation. With a clear grasp of the concept of information in hand, Timpson turns his attention to the pressing question of whether advances in quantum information theory pave the way for the resolution of the traditional conceptual problems of quantum mechanics: the deep problems which loom over measurement, nonlocality and the general nature of quantum ontology. He marks out a number of common pitfalls to be avoided before analysing in detail some concrete proposals, including the radical quantum Bayesian programme of Caves, Fuchs, and Schack. One central moral which is drawn is that, for all the interest that the quantum information-inspired approaches hold, no cheap resolutions to the traditional problems of quantum mechanics are to be had. Book jacket Cover Contents 1 Introduction 2 What is Information? 2.1 How to talk about information: Some simple ways 2.2 The Shannon Information and related concepts 2.2.1 Warming up 2.2.2 Formal development of the theory; and the definition of Informationt 2.2.3 Information and Uncertainty 2.2.4 More on the communication channel 2.2.5 Mutual informationt and flow 2.3 Alternative approaches: Dretske and Semantic Naturalism 2.3.1 Dretske’s information that 2.4 Summary 3 Quantum Information Theory 3.1 Introduction 3.2 Bits and qubits 3.3 The no-cloning theorem 3.4 Entanglement-assisted communication 3.5 Quantum computers 3.6 What is quantum information? 3.6.1 Quantum sources: how much 3.6.2 Quantum sources: what 3.6.3 An objection: Jozsa’s argument 3.7 The worldliness of quantum information 3.7.1 Information and the physical 3.8 Summary 4 Case Study: Teleportation 4.1 Introduction 4.2 The quantum teleportation protocol 4.2.1 Some information-theoretic aspects of teleportation 4.3 The puzzles of teleportation 4.4 Resolving (dissolving) the problem 4.4.1 The simulation fallacy 4.5 The teleportation process under di.erent interpretations 4.5.1 Collapse interpretations: Dirac/von Neumann, GRW 4.5.2 No collapse and no extra values: Everett 4.5.3 No collapse, but extra values: Bohm 4.5.4 Ensemble and statistical viewpoints 4.6 Concluding remarks 5 The Deutsch–Hayden Approach: Nonlocality, Entanglement, and Information Flow 5.1 Introduction 5.2 The Deutsch–Hayden Picture 5.2.1 Locality claim (2): Contiguity 5.3 Assessing the Claims to Locality 5.3.1 The Conservative Interpretation 5.3.2 The Ontological Interpretation 5.4 Information and Information Flow 5.4.1 Whereabouts of information 5.4.2 Explaining informationt flow in teleportation: Locally accessible and inaccessible informationt 5.4.3 Assessing the claims for information flow 5.5 Conclusion 6 Quantum Computation and the Church–Turing Hypothesis 6.1 Introduction 6.2 Quantum computation and containing information 6.3 The Turing Principle versus the Church–Turing Hypothesis 6.3.1 Non-Turing computability? The example of Malament– Hogarth spacetimes 6.3.2 Lessons 6.4 The Church–Turing Hypothesis as a constraint on physics? 6.5 Message 7 Information and the Foundations of Quantum Mechanics: Preliminaries 7.1 Information Talk in Quantum Mechanics 8 Some Information-Theoretic Approaches 8.1 Introduction 8.2 Zeilinger’s Foundational Principle 8.2.1 Word and world: Semantic ascent 8.2.2 Where next? 8.3 The Clifton–Bub–Halvorson characterization theorem 8.3.1 The setting 8.3.2 Some queries regarding the C*-algebraic starting point 8.3.3 Questions of Interpretation 8.4 Further Developments: Generalized Probability Theories 8.5 Conclusion 9 Quantum Bayesianism 1: The Proposal 9.1 Introduction 9.2 Setting the Scene 9.2.1 An outline of the position 9.2.2 In more detail 9.2.3 From information to belief 9.2.4 Two hints 9.3 Not solipsism; and not instrumentalism, either 9.4 Summary: The virtues 10 Quantum Bayesianism 2: Challenges 10.1 What’s the ontology? 10.1.1 Objectivity and the classical level 10.1.2 Quantum states for classical objects 10.2 Troubles with explanation 10.3 Subjective probabilities 10.3.1 A Quantum Bayesian Moore’s Paradox 10.3.2 The means/ends objection 10.4 Conclusions 11 Conclusions A: A Review of the Quantum Formalism A.1 Hilbert Space and Linear Operators A.2 States and Measurement B: Generalized Uncertainty Measures: Uffink’s Axioms B.1 The Uncertainty Measures Ur(P,μ) B.2 Uniqueness arguments for the Shannon Information B.3 Majorization and entropic criteria for entanglement Bibliography Index A B C D E F G H I J K L M N O P Q R S T U V W Y Z Christopher G. Timpson Provides A Full-length Philosophical Treatment Of Quantum Information Theory And The Questions It Raises For Our Understanding Of The Quantum World. He Argues For An Ontologically Deflationary Account Of The Nature Of Quantum Information, Which Is Grounded In A Revisionary Analysis Of The Concepts Of Information. Introduction -- What Is Information? -- Quantum Information Theory -- Case Study : Teleportation -- The Deutsch-hayden Approach : Nonlocality, Entanglement, And Information Flow -- Quantum Computation And The Church-turing Hypothesis -- Information And The Foundations Of Quantum Mechanics : Preliminaries -- Some Information-theoretic Approaches -- Quantum Bayesianism 1 : The Proposal -- Quantum Bayesianism 2 : Challenges -- Conclusions -- [appendix] A. A Review Of The Quantum Formalism -- [appendix] B. Generalized Uncertainty Measures : Uffink's Axioms. Christopher G. Timpson. Includes Bibliographical References (p. [265]-284) And Index.