Comparing different non-Markovianity measures in a driven qubit system

Abstract

We consider two recently proposed measures of non-Markovianity applied to a particular quantum process describing the dynamics of a driven qubit in a structured reservoir. The motivation of this study is twofold: on one hand, we study the differences and analogies of the non-Markovianity measures and on the other hand, we investigate the effect of the driving force on the dissipative dynamics of the qubit. In particular we ask if the drive introduces new channels for energy and/or information transfer between the system and the environment, or amplifies existing ones. We show under which conditions the presence of the drive slows down the inevitable loss of quantum properties of the qubit.

Measures of non-Markovianity: Divisibility versus backflow of information

“…We performed explicit construction showing that in general these two measures do not agree supporting [17][18][19].…”

“…The converse is in general not true. This problem was carefully analyzed in the paper [19] for phenomenological integro-differential master equations and in the recent paper [17], where the authors have studied the non-Markovian character of a driven qubit in a structured reservoir in different dynamical regime using N RHP (Λ) and N BLP (Λ).…”

“…It is clear that RHP characterize a mathematical property of the dynamical map whereas the idea of BLP is based on physical features of the system-reservoir interaction, rather than the mathematical properties of the dynamical map of the open system. In a recent paper [17] Haikka, Cresser and Maniscalco performed detailed analysis of these approaches studying the dynamics of the driven qubit in a structured environment. It is indicated [17] that the concepts of RHP and BLP need not agree, as was also conjectured in [18] and checked in [19].…”

“…In a recent paper [17] Haikka, Cresser and Maniscalco performed detailed analysis of these approaches studying the dynamics of the driven qubit in a structured environment. It is indicated [17] that the concepts of RHP and BLP need not agree, as was also conjectured in [18] and checked in [19]. BLP measure was recently analyzed for the dynamics of a qubit coupled to a spin environment via an energy-exchange mechanism [20].…”

Investigating the generality of time-local master equations

“…Even though non-Markovian behavior appears in many branches of physics, there is no definition of nonMarkovianity that is generally agreed upon. Several measures of non-Markovianity have been proposed [8][9][10][11] and have been compared [12,13].…”