Information and Entropy in Quantum Theory

Abstract

We look at certain thought experiments based upon the 'delayed choice' and 'quantum eraser' interference experiments, which present a complementarity between information gathered from a quantum measurement and interference effects. It has been argued that these experiments show the Bohm interpretation of quantum theory is untenable. We demonstrate that these experiments depend critically upon the assumption that a quantum optics device can operate as a measuring device, and show that, in the context of these experiments, it cannot be consistently understood in this way. By contrast, we then show how the notion of 'active information' in the Bohm interpretation provides a coherent explanation of the phenomena shown in these experiments. We then examine the relationship between information and entropy. The thought experiment connecting these two quantities is the Szilard Engine version of Maxwell's Demon, and it has been suggested that quantum measurement plays a key role in this. We provide the first complete description of the operation of the Szilard Engine as a quantum system. This enables us to demonstrate that the role of quantum measurement suggested is incorrect, and further, that the use of information theory to resolve Szilard's paradox is both unnecessary and insufficient. Finally we show that, if the concept of 'active information' is extended to cover thermal density matrices, then many of the conceptual problems raised by this paradox appear to be resolved.

PhD Thesis, 2002. 306 pages. 43 figures

References in corpus (15)

• Quantum Copying: Beyond the No-Cloning Theorem
• Optimal Quantum Cloning Machines
• Operationally Invariant Information in Quantum Measurements
• Quantum mechanical Carnot engine
• Spin flips and quantum information for anti-parallel spins
• Minimal optimal generalized quantum measurements
• Optimal minimal measurements of mixed states
• Collective versus local measurements on two parallel or antiparallel spins
• Reversible Simulation of Irreversible Computation by Pebble Games
• Can the Decoherent Histories Description of Reality be Considered Satisfactory?
• About the Notion of Truth in the Decoherent Histories Approach: a reply to Griffiths
• Universality of optimal measurements
• Consistent Histories and the Bohm Approach
• Quantum Measurement and Shannon Information, A Reply to M. J. W. Hall
• Comment on "Conceptual Inadequacy of Shannon Information ..." by C. Brukner and A. Zeilinger

Cited by in corpus (8)

• Generalising Landauer's Principle
• A new pilot-wave model for quantum field theory
• Quantum- vs. Macro- Realism: What does the Leggett-Garg Inequality actually test?
• Does a Computer have an Arrow of Time?
• The Physical Basis of the Gibbs-von Neumann entropy
• Entropy for theories with indefinite causal structure
• Are all reversible computations tidy?
• The (absence of a) relationship between thermodynamic and logical reversibility