Non-Markovian dynamics of open quantum systems
Abstract
This thesis is centred around the striking phenomenon of non-Markovianity
which emanates from exact dynamical descriptions of open quantum systems. Non-
Markovianity is associated with the existence of memory effects in the environment
and leads to a partial recovery of information of the system, temporarily counteracting
the deleterious effect of the surrounding environment. We devote this thesis to
addressing two fundamental questions surrounding the topic of non-Markovianity.
The first is concerned with how to evaluate the extent to which a specific dynamics is
non-Markovian, in terms of a physically meaningful and easily computable measure.
In literature, the desire to quantify non-Markovianity has motivated a plethora of
measures which provide unique, albeit potentially contradicting, interpretations of
memory effects. In an attempt to consolidate the literature, we introduce and critically
compare several recently proposed non-Markovianity measures for single qubit
and two qubit systems in both pure dephasing and dissipative scenarios. The second
question explores the natural optimism of the usefulness of non-Markovianity as a
resource in quantum information protocols. In more detail, we study whether memory
effects combined with external control techniques offer a possibility to exploit
non-Markovianity for an overall superior technique to combat decoherence. The
standard approach for Markovian dynamics involves the critical assumption of dissipative
dynamics which are fixed in the presence of control. We expose the serious
pitfalls in experimentally implementing such a strategy in realistic non-Markovian
scenarios and accentuate the importance of using exact approaches in non-Markovian
control theory. Using an exact description of a pure dephasing system subject to dynamical
decoupling protocols, we demonstrate that contrary to intuitive reasoning,
non-Markovianity is not trivially a resource.