Effects of initial system-environment correlations on open quantum system dynamics and state preparation

TL;DR

This paper studies how initial correlations between a quantum system and its environment influence the system's state preparation, using an extended Liouville space method to analyze non-Markovian dynamics and trace distance bounds.

Contribution

It introduces an efficient extended Liouville space approach and bounds for trace distance to better understand initial system-environment correlations in quantum dynamics.

Findings

Initial correlations significantly affect state preparation outcomes.

Derived bounds provide conditions for trace distance increase related to non-Markovianity.

Method effectively describes non-Markovian dynamics under strong fields.

Abstract

We investigate the preparation of a target initial state for a two-level (qubit) system from a system-environment equilibrium or correlated state by an external field. The system-environment equilibrium or correlated state results from the inevitable interaction of the system with its environment. An efficient method in an extended auxiliary Liouville space is introduced to describe the dynamics of the non-Markovian open quantum system in the presence of a strong field and an initial system-environment correlation. By using the time evolutions of the population difference, the state trajectory in the Bloch sphere representation and the trace distance between two reduced system states of the open quantum system, the effect of initial system-environment correlations on the preparation of a system state is studied. We introduce an upper bound and a lower bound for the trace distance within our perturbation formalism to describe the diverse behaviors of the dynamics of the trace distance between various correlated states after the system state preparation. These bounds that are much more computable than similar bounds in the literature give a sufficient condition and a necessary condition for the increase of the trace distance and are related to the witnesses of non-Markovianity and initial system-bath correlation.