Comparison of non-Markovianity criteria in a qubit system under random external fields

TL;DR

This paper compares various criteria for detecting non-Markovianity in a qubit system influenced by random external fields, demonstrating their agreement in both non-dissipative and dissipative scenarios.

Contribution

It introduces a map and master equation for a qubit under random fields and compares non-Markovianity criteria, highlighting their consistency across different conditions.

Findings

Criteria agree in non-dissipative case

Criteria agree with population damping

Provides a framework for analyzing non-Markovianity in qubits

Abstract

We give the map representing the evolution of a qubit under the action of non-dissipative random external fields. From this map we construct the corresponding master equation that in turn allows us to phenomenologically introduce population damping of the qubit system. We then compare, in this system, the time-regions when non-Markovianity is present on the basis of different criteria both for the non-dissipative and dissipative case. We show that the adopted criteria agree both in the non-dissipative case and in the presence of population damping.