Information and entropy in quantum theory
Recent developments in quantum computing have revived interest in the notion of information
as a foundational principle in physics. It has been suggested that information provides a means of
interpreting quantum theory and a means of understanding the role of entropy in thermodynamics.
The thesis presents a critical examination of these ideas, and contrasts the use of Shannon
information with the concept of 'active information' introduced by Bohm and Hiley.
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.