Non-Markovian dynamics of open quantum systems

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

Coherence trapping and information back-flow in dephasing qubits

We study the interplay between coherence trapping, information back-flow and the form of the reservoir spectral density for dephasing qubits. We show that stationary coherence is maximized when the qubit undergoes non-Markovian dynamics, and we elucidate the different roles played by the low and high frequency parts of the environmental spectrum. We show that the low frequencies fully determine the presence or absence of information back-flow while the high frequencies dictate the maximal amount of coherence trapping.Comment: 4 pages, 3 figures. New references have been added to the introduction. Also including minor modification

Dynamical decoupling efficiency versus quantum non-Markovianity

We investigate the relationship between non-Markovianity and the effectiveness of a dynamical decoupling protocol for qubits undergoing pure dephasing. We consider an exact model in which dephasing arises due to a bosonic environment with a spectral density of the Ohmic class. This is parametrised by an Ohmicity parameter by changing which we can model both Markovian and non-Markovian environments. Interestingly, we find that engineering a non-Markovian environment is detrimental to the efficiency of the dynamical decoupling scheme, leading to a worse coherence preservation. We show that each dynamical decoupling pulse reverses the flow of quantum information and, on this basis, we investigate the connection between dynamical decoupling efficiency and the reservoir spectral density. Finally, in the spirit of reservoir engineering, we investigate the optimum system-reservoir parameters for achieving maximum stationary coherences.Comment: 6 pages, 4 figure

Problem of coherent control in non-Markovian open quantum systems

We critically evaluate the most widespread assumption in the theoretical description of coherent control strategies for open quantum systems. We show that, for non-Markovian open systems dynamics, this fixed-dissipator assumption leads to a serious pitfall generally causing difficulties in the effective modeling of the controlled system. We show that at present, to avoid these problems, a full microscopic description of the controlled system in the presence of noise may often be necessary. We illustrate our findings with a paradigmatic example.</p

Dynamics of incompatibility of quantum measurements in open systems

The non-classical nature of quantum states, often illustrated using entanglement measures or quantum discord, constitutes a resource for quantum information protocols. However, the non-classicality of a quantum system cannot be encapsulated as a property of the state alone, as the set of available measurements used to extract information on the system is typically restricted. In this work we study how the non-classicality of quantum measurements, quantified via their incompatibility, is influenced by quantum noise and, further, how a non-Markovian environment may help us in maintaining the measurement resources.Comment: v2: presentation improved and typos correcte

Dynamical memory effects in correlated quantum channels

Memory effects play a fundamental role in the study of the dynamics of open quantum systems. There exist two conceptually distinct notions of memory discussed for quantum channels in the literature. In quantum information theory quantum channels with memory are characterized by the existence of correlations between successive applications of the channel on a sequence of quantum systems. In open quantum systems theory memory effects arise dynamically during the time evolution of quantum systems and define non-Markovian dynamics. Here we relate and combine these two different concepts of memory. In particular, we study the interplay between correlations between multiple uses of quantum channels and non-Markovianity as nondivisibility of the t-parametrized family of channels defining the dynamical map.Peer reviewe

Erwerbsverflechtungen im laendlichen Raum: Fallstudie Nordosthessen-Meissner

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