Precursors of non-Markovianity

Abstract

Using the paradigm of information backflow to characterize a non-Markovian evolution, we introduce so-called precursors of non-Markovianity, i.e. necessary properties that the system and environment state must exhibit at earlier times in order for an ensuing dynamics to be non-Markovian. In particular, we consider a quantitative framework to assess the role that established system-environment correlations together with changes in environmental states play in an emerging non-Markovian dynamics. By defining the relevant contributions in terms of the Bures distance, which is conveniently expressed by means of the quantum state fidelity, these quantities are well defined and easily applicable to a wide range of physical settings. We exemplify this by studying our precursors of non-Markovianity in discrete and continuous variable non-Markovian collision models.

On the connection between microscopic description and memory effects in open quantum system dynamics

“…On the other hand, in a complementary way, we can use the bound in Eq. (4) as a starting point to gain some quantitative information about the systemenvironment correlations and the changes in the environment established by the interaction, via measurements performed on the reduced system only [21][22][23].…”

“…Within the trace distance approach, it is possible to ascribe any backflow of information towards the open system to either the generation of system-environment correlations, or changes in the environmental state due to the interaction with the open system, or both [7,20]. Even more, quantitative links between the trace distance variations and the influence of both system-environmental correlations and environmental changes, as measured via the trace distance, have been derived [21][22][23], and a similar result has recently been obtained also for entropic distinguishability quantifiers [24]. In addition to their quantitative content, these links suggest further evidence that the possible quantum nature of the system-environment correlations, in terms of the presence of entanglement [25] or non-zero discord [26][27][28], does not play any special role in producing memory effects, compared to mere classical correlations [29,30].…”

Quantum synchronization in a collision model

“…Among numerous ways to simulate open quantum systems, collision models have recently attracted considerable attention due to their versatility in modeling different regimes of the dynamics, such as with or without memory [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48], which is much harder to implement with other approaches. In a collision model framework, the environment is constituted by a number of particles, which can be both finite dimensional and continuous variable, and the dynamics of the system is determined by its sequential interaction with these environmental units.…”

Não Markovianidade em modelos colisionais Gaussianos

“…In Ref. [66], the authors asked, within a collisional model context, whether it was possible to pinpoint the backflow of information to either changes in the environmental states, or the buildup of correlations between system and environment. This question is relevant since these are the two main ingredients entering in the 2nd law of thermodynamics in the quantum domain [118,119].…”

“…The first is to consider that the ancillas already start correlated [53][54][55][56][57]. The other one is to assume information is transmitted between the ancillas during the process [58][59][60][61][62][63][64][65][66]. In this dissertation, we shall focus on the second case.…”