Information Flow, Non-Markovianity and Geometric Phases

TL;DR

This paper investigates the relationship between geometric phases and information flow in a two-level quantum system, revealing how environmental interactions influence quantum phase behavior and non-Markovian effects.

Contribution

It provides an analytic relation for pure states and numerical insights for mixed states linking geometric phases with information flow in open quantum systems.

Findings

Geometric phase varies with information flow direction.

Analytic relation established for pure initial states.

Numerical results for mixed initial states.

Abstract

Geometric phases and information flows of a two-level system coupled to its environment are calculated and analyzed. The information flow is defined as a cumulant of changes in trace distance between two quantum states, which is similar to the measure for non-Markovianity given by Breuer. We obtain an analytic relation between the geometric phase and the information flow for pure initial states, and a numerical result for mixed initial states. The geometric phase behaves differently depending on whether there are information flows back to the two-level system from its environment.