Information and Entropy in Quantum Theory

TL;DR

This paper critically examines thought experiments involving quantum measurement and information, challenges common assumptions, and demonstrates how the Bohm interpretation and active information provide coherent explanations, ultimately addressing the quantum Szilard Engine paradox.

Contribution

It offers a new analysis of quantum measurement experiments, clarifies the role of active information in Bohm's interpretation, and provides a complete quantum description of the Szilard Engine.

Findings

Quantum optics devices cannot be considered as measuring devices in these experiments.

Active information in Bohm's interpretation coherently explains the phenomena.

Quantum measurement is not essential for resolving Szilard's paradox.

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.