Equivalence of the measures of non-Markovianty for open two-level systems

TL;DR

This paper proves that three different measures of non-Markovianity are equivalent for open two-level quantum systems in common models, simplifying their application and confirming they capture the same intrinsic non-Markovian features.

Contribution

It demonstrates the equivalence of three non-Markovianity measures for two-level systems under specific models, and shows the maximization step can be omitted without loss of sensitivity.

Findings

The three measures have identical non-Markovian time intervals.

The measures are equivalent for Jaynes-Cummings and dephasing models.

Maximization in the first measure can be removed without affecting detection sensitivity.

Abstract

In order to depict the deviation of quantum time evolution in open systems from Markovian processes, different measures have been presented. We demonstrate that the measure proposed by Breuer, Laine and Piilo [Phys. Rev. Lett. 103, 210401 (2009)] and the two measures proposed by Rivas, Huelga and Plenio [Phys. Rev. Lett. 105, 050403 (2010)] have exactly the same non-Markovian time-evolution intervals and thus are really equivalent each other when they apply to open two-level systems coupled to environments via Jaynes-Cummings or dephasing models. This equivalence implies that the three measures in different ways capture the intrinsical characters of non-Markovianty of quantum evolutional processes. We also show that the maximization in the definition of the first measure can be actually removed for the considered models without influencing the sensibility of the measure to detect non-Markovianty.