Decoherence in an exactly solvable qubit model with initial qubit-environment correlations

TL;DR

This paper provides exact solutions for the decoherence dynamics of a qubit coupled to a harmonic oscillator bath, considering correlated initial states, and analyzes how initial correlations affect decoherence and entropy evolution.

Contribution

It extends previous models by deriving exact solutions for a broad class of correlated initial states in qubit-bath systems.

Findings

Exact expressions for off-diagonal density matrix elements

Initial correlations significantly influence decoherence behavior

Analysis of entropy dynamics during decoherence

Abstract

We study a model of dephasing (decoherence) in a two-state quantum system (qubit) coupled to a bath of harmonic oscillators. An exact analytic solution for the reduced dynamics of a two-state system in this model has been obtained previously for factorizing initial states of the combined system. We show that the model admits exact solutions for a large class of correlated initial states which are typical in the theory of quantum measurements. We derive exact expressions for the off-diagonal elements of the qubit density matrix, which hold for an arbitrary strength of coupling between the qubit and the bath. The influence of initial correlations on decoherence is considered for different bath spectral densities. Time behavior of the qubit entropy in the decoherence process is discussed.