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.