Decoherence and Localization in Quantum Two-Level Systems

TL;DR

This paper compares various approaches to decoherence and localization in quantum two-level systems, highlighting their connections and analyzing the degree of decoherence in different frameworks.

Contribution

It establishes a close connection between decoherent histories and quantum jump simulation, and discusses decoherence levels in these approaches.

Findings

Decoherent histories and quantum jump simulation are closely connected.

The degree of approximate decoherence is analyzed in detail.

Connections with quantum state diffusion are also discussed.

Abstract

We study and compare the decoherent histories approach, the environment-induced decoherence and the localization properties of thesolutions to the stochastic Schr\"{o}dinger equation in quantum jump simulationand quantum state diffusion approaches, for a quantum two-level system model. We show, in particular, that there is a close connection between the decoherent histories and the quantum jump simulation, complementing a connection with the quantum state diffusion approach noted earlier by Di\'{o}si, Gisin, Halliwell and Percival. In the case of the decoherent histories analysis, the degree of approximate decoherence is discussed in detail.