Foundations of Quantum Decoherence

TL;DR

This paper rigorously derives the master equation for quantum Brownian motion from foundational principles, clarifying the quantum-classical transition crucial for quantum computing and decoherence understanding.

Contribution

It provides a self-contained, axiomatic derivation of the quantum Brownian motion master equation, advancing the foundational understanding of quantum decoherence.

Findings

Quantum decoherence models the quantum-to-classical transition effectively.

The derivation is based on minimal quantum axioms, ensuring rigor.

The master equation accurately describes physical examples of decoherence.

Abstract

The conventional interpretation of quantum mechanics, though it permits a correspondence to classical physics, leaves the exact mechanism of transition unclear. Though this was only of philosophical importance throughout the twentieth century, over the past decade new technological developments, such as quantum computing, require a more thorough understanding of not just the result of quantum emergence, but also its mechanism. Quantum decoherence theory is the model that developed out of necessity to deal with the quantum-classical transition explicitly, and without external observers. In this thesis, we present a self-contained and rigorously argued full derivation of the master equation for quantum Brownian motion, one of the key results in quantum decoherence theory. We accomplish this from a foundational perspective, only assuming a few basic axioms of quantum mechanics and deriving their consequences. We then consider a physical example of the master equation and show that quantum decoherence successfully represents the transition from a quantum to classical system.