Non-Markovianity and Quantum Correlations in Qubit-Systems

In this Thesis I discuss the exact dynamics of simple non-Markovian systems. I focus on fundamental questions at the core of non-Markovian theory and investigate the dynamics of quantum correlations under non-Markovian decoherence. In the first context I present the connection between two different non-Markovian approaches, and compare two distinct definitions of non-Markovianity. The general aim is to characterize in exemplary cases which part of the environment is responsible for the feedback of information typical of non- Markovian dynamics. I also show how such a feedback of information is not always described by certain types of master equations commonly used to tackle non-Markovian dynamics. In the second context I characterize the dynamics of two qubits in a common non-Markovian reservoir, and introduce a new dynamical effect in a wellknown model, i.e., two qubits under depolarizing channels. In the first model the exact solution of the dynamics is found, and the entanglement behavior is extensively studied. The non-Markovianity of the reservoir and reservoirmediated-interaction between the qubits cause non-trivial dynamical features. The dynamical interplay between different types of correlations is also investigated. In the second model the study of quantum and classical correlations demonstrates the existence of a new effect: the sudden transition between classical and quantum decoherence. This phenomenon involves the complete preservation of the initial quantum correlations for long intervals of time of the order of the relaxation time of the system.

Dialogue in the crisis of representation : realism and antirealism in the context of the conversation between theologians and quantum physicists in Göttingen 1949-1961

The aim of this study is to analyse the content of the interdisciplinary conversations in Göttingen between 1949 and 1961. The task is to compare models for describing reality presented by quantum physicists and theologians. Descriptions of reality indifferent disciplines are conditioned by the development of the concept of reality in philosophy, physics and theology. Our basic problem is stated in the question: How is it possible for the intramental image to match the external object?Cartesian knowledge presupposes clear and distinct ideas in the mind prior to observation resulting in a true correspondence between the observed object and the cogitative observing subject. The Kantian synthesis between rationalism and empiricism emphasises an extended character of representation. The human mind is not a passive receiver of external information, but is actively construing intramental representations of external reality in the epistemological process. Heidegger's aim was to reach a more primordial mode of understanding reality than what is possible in the Cartesian Subject-Object distinction. In Heidegger's philosophy, ontology as being-in-the-world is prior to knowledge concerning being. Ontology can be grasped only in the totality of being (Dasein), not only as an object of reflection and perception. According to Bohr, quantum mechanics introduces an irreducible loss in representation, which classically understood is a deficiency in knowledge. The conflicting aspects (particle and wave pictures) in our comprehension of physical reality, cannot be completely accommodated into an entire and coherent model of reality. What Bohr rejects is not realism, but the classical Einsteinian version of it. By the use of complementary descriptions, Bohr tries to save a fundamentally realistic position. The fundamental question in Barthian theology is the problem of God as an object of theological discourse. Dialectics is Barth¿s way to express knowledge of God avoiding a speculative theology and a human-centred religious self-consciousness. In Barthian theology, the human capacity for knowledge, independently of revelation, is insufficient to comprehend the being of God. Our knowledge of God is real knowledge in revelation and our words are made to correspond with the divine reality in an analogy of faith. The point of the Bultmannian demythologising programme was to claim the real existence of God beyond our faculties. We cannot simply define God as a human ideal of existence or a focus of values. The theological programme of Bultmann emphasised the notion that we can talk meaningfully of God only insofar as we have existential experience of his intervention. Common to all these twentieth century philosophical, physical and theological positions, is a form of anti-Cartesianism. Consequently, in regard to their epistemology, they can be labelled antirealist. This common insight also made it possible to find a common meeting point between the different disciplines. In this study, the different standpoints from all three areas and the conversations in Göttingen are analysed in the frameworkof realism/antirealism. One of the first tasks in the Göttingen conversations was to analyse the nature of the likeness between the complementary structures inquantum physics introduced by Niels Bohr and the dialectical forms in the Barthian doctrine of God. The reaction against epistemological Cartesianism, metaphysics of substance and deterministic description of reality was the common point of departure for theologians and physicists in the Göttingen discussions. In his complementarity, Bohr anticipated the crossing of traditional epistemic boundaries and the generalisation of epistemological strategies by introducing interpretative procedures across various disciplines.

Non-Markovian Dynamics in Continuous Variable Quantum Systems

The present manuscript represents the completion of a research path carried forward during my doctoral studies in the University of Turku. It contains information regarding my scientific contribution to the field of open quantum systems, accomplished in collaboration with other scientists. The main subject investigated in the thesis is the non-Markovian dynamics of open quantum systems with focus on continuous variable quantum channels, e.g. quantum Brownian motion models. Non-Markovianity is here interpreted as a manifestation of the existence of a flow of information exchanged by the system and environment during the dynamical evolution. While in Markovian systems the flow is unidirectional, i.e. from the system to the environment, in non-Markovian systems there are time windows in which the flow is reversed and the quantum state of the system may regain coherence and correlations previously lost. Signatures of a non-Markovian behavior have been studied in connection with the dynamics of quantum correlations like entanglement or quantum discord. Moreover, in the attempt to recognisee non-Markovianity as a resource for quantum technologies, it is proposed, for the first time, to consider its effects in practical quantum key distribution protocols. It has been proven that security of coherent state protocols can be enhanced using non-Markovian properties of the transmission channels. The thesis is divided in two parts: in the first part I introduce the reader to the world of continuous variable open quantum systems and non-Markovian dynamics. The second part instead consists of a collection of five publications inherent to the topic.

Non-Markovian Dynamics and the Quantum-To-Classical Transition for Quantum Brownian Motion

In this Thesis I discuss the dynamics of the quantum Brownian motion model in harmonic potential. This paradigmatic model has an exact solution, making it possible to consider also analytically the non-Markovian dynamics. The issues covered in this Thesis are themed around decoherence. First, I consider decoherence as the mediator of quantum-to-classical transition. I examine five different definitions for nonclassicality of quantum states, and show how each definition gives qualitatively different times for the onset of classicality. In particular I have found that all characterizations of nonclassicality, apart from one based on the interference term in the Wigner function, result in a finite, rather than asymptotic, time for the emergence of classicality. Second, I examine the diverse effects which coupling to a non-Markovian, structured reservoir, has on our system. By comparing different types of Ohmic reservoirs, I derive some general conclusions on the role of the reservoir spectrum in both the short-time and the thermalization dynamics. Finally, I apply these results to two schemes for decoherence control. Both of the methods are based on the non-Markovian properties of the dynamics.

Quantum Tomography with Phase Space Measurements

This thesis addresses the use of covariant phase space observables in quantum tomography. Necessary and sufficient conditions for the informational completeness of covariant phase space observables are proved, and some state reconstruction formulae are derived. Different measurement schemes for measuring phase space observables are considered. Special emphasis is given to the quantum optical eight-port homodyne detection scheme and, in particular, on the effect of non-unit detector efficiencies on the measured observable. It is shown that the informational completeness of the observable does not depend on the efficiencies. As a related problem, the possibility of reconstructing the position and momentum distributions from the marginal statistics of a phase space observable is considered. It is shown that informational completeness for the phase space observable is neither necessary nor sufficient for this procedure. Two methods for determining the distributions from the marginal statistics are presented. Finally, two alternative methods for determining the state are considered. Some of their shortcomings when compared to the phase space method are discussed.

Optimizing Customer Energy Invoice Calculation with Parallel Computation

Diplomityön tarkoituksena on optimoida asiakkaiden sähkölaskun laskeminen hajautetun laskennan avulla. Älykkäiden etäluettavien energiamittareiden tullessa jokaiseen kotitalouteen, energiayhtiöt velvoitetaan laskemaan asiakkaiden sähkölaskut tuntiperusteiseen mittaustietoon perustuen. Kasvava tiedonmäärä lisää myös tarvittavien laskutehtävien määrää. Työssä arvioidaan vaihtoehtoja hajautetun laskennan toteuttamiseksi ja luodaan tarkempi katsaus pilvilaskennan mahdollisuuksiin. Lisäksi ajettiin simulaatioita, joiden avulla arvioitiin rinnakkaislaskennan ja peräkkäislaskennan eroja. Sähkölaskujen oikeinlaskemisen tueksi kehitettiin mittauspuu-algoritmi.

Quantum Hall effect in 2 dimensional GaInAs structure

Transport properties of GaAs / δ – Mn / GaAs / InxGa1-xAs / GaAs structure with Mn δ – layer, which is separated from InxGa1-xAs quantum well (QW) by 3 nm thick GaAs spacer was investigated. This structure with high mobility was characterized by X-ray difractometry and reflectometry. Transport and electrical properties of the structure were measured by using Pulsed Magnetic Field System (PMFS). During investigation of the Shubnikov – de Haas and the Hall effects the main parameters of QW structure such as cyclotron mass, Fermi level, g – factor, Dingle temperature and concentration of holes were estimated. Obtained results show high quality of the prepared structure. However, anomalous Hall effect at temperatures 2.09 K, 3 K, 4.2 K is not clearly observed. Attempts to identify magnetic moment were made. For this purpose the polarity of the filed was changed to the opposite at each shot. As a result hysteresis loop was not observed in the magnetic field dependences of the anomalous Hall resistivity.This can be attributed to the imperfection of the experimental setup.

Non-Markovian dynamics and quantum information probes

This Thesis discusses the phenomenology of the dynamics of open quantum systems marked by non-Markovian memory effects. Non-Markovian open quantum systems are the focal point of a flurry of recent research aiming to answer, e.g., the following questions: What is the characteristic trait of non-Markovian dynamical processes that discriminates it from forgetful Markovian dynamics? What is the microscopic origin of memory in quantum dynamics, and how can it be controlled? Does the existence of memory effects open new avenues and enable accomplishments that cannot be achieved with Markovian processes? These questions are addressed in the publications forming the core of this Thesis with case studies of both prototypical and more exotic models of open quantum systems. In the first part of the Thesis several ways of characterizing and quantifying non-Markovian phenomena are introduced. Their differences are then explored using a driven, dissipative qubit model. The second part of the Thesis focuses on the dynamics of a purely dephasing qubit model, which is used to unveil the origin of non-Markovianity for a wide class of dynamical models. The emergence of memory is shown to be strongly intertwined with the structure of the spectral density function, as further demonstrated in a physical realization of the dephasing model using ultracold quantum gases. Finally, as an application of memory effects, it is shown that non- Markovian dynamical processes facilitate a novel phenomenon of timeinvariant discord, where the total quantum correlations of a system are frozen to their initial value. Non-Markovianity can also be exploited in the detection of phase transitions using quantum information probes, as shown using the physically interesting models of the Ising chain in a transverse field and a Coulomb chain undergoing a structural phase transition.

Memory Effects in the Dynamics of Open Quantum Systems

In this Thesis various aspects of memory effects in the dynamics of open quantum systems are studied. We develop a general theoretical framework for open quantum systems beyond the Markov approximation which allows us to investigate different sources of memory effects and to develop methods for harnessing them in order to realise controllable open quantum systems. In the first part of the Thesis a characterisation of non-Markovian dynamics in terms of information flow is developed and applied to study different sources of memory effects. Namely, we study nonlocal memory effects which arise due to initial correlations between two local environments and further the memory effects induced by initial correlations between the open system and the environment. The last part focuses on describing two all-optical experiment in which through selective preparation of the initial environment states the information flow between the system and the environment can be controlled. In the first experiment the system is driven from the Markovian to the non- Markovian regime and the degree of non-Markovianity is determined. In the second experiment we observe the nonlocal nature of the memory effects and provide a novel method to experimentally quantify frequency correlations in photonic environments via polarisation measurements.

Design Space Exploration for MPSoC Architectures

Multiprocessor system-on-chip (MPSoC) designs utilize the available technology and communication architectures to meet the requirements of the upcoming applications. In MPSoC, the communication platform is both the key enabler, as well as the key differentiator for realizing efficient MPSoCs. It provides product differentiation to meet a diverse, multi-dimensional set of design constraints, including performance, power, energy, reconfigurability, scalability, cost, reliability and time-to-market. The communication resources of a single interconnection platform cannot be fully utilized by all kind of applications, such as the availability of higher communication bandwidth for computation but not data intensive applications is often unfeasible in the practical implementation. This thesis aims to perform the architecture-level design space exploration towards efficient and scalable resource utilization for MPSoC communication architecture. In order to meet the performance requirements within the design constraints, careful selection of MPSoC communication platform, resource aware partitioning and mapping of the application play important role. To enhance the utilization of communication resources, variety of techniques such as resource sharing, multicast to avoid re-transmission of identical data, and adaptive routing can be used. For implementation, these techniques should be customized according to the platform architecture. To address the resource utilization of MPSoC communication platforms, variety of architectures with different design parameters and performance levels, namely Segmented bus (SegBus), Network-on-Chip (NoC) and Three-Dimensional NoC (3D-NoC), are selected. Average packet latency and power consumption are the evaluation parameters for the proposed techniques. In conventional computing architectures, fault on a component makes the connected fault-free components inoperative. Resource sharing approach can utilize the fault-free components to retain the system performance by reducing the impact of faults. Design space exploration also guides to narrow down the selection of MPSoC architecture, which can meet the performance requirements with design constraints.

Universal Quantum Cloning

After introducing the no-cloning theorem and the most common forms of approximate quantum cloning, universal quantum cloning is considered in detail. The connections it has with universal NOT-gate, quantum cryptography and state estimation are presented and briefly discussed. The state estimation connection is used to show that the amount of extractable classical information and total Bloch vector length are conserved in universal quantum cloning. The 1  2 qubit cloner is also shown to obey a complementarity relation between local and nonlocal information. These are interpreted to be a consequence of the conservation of total information in cloning. Finally, the performance of the 1  M cloning network discovered by Bužek, Hillery and Knight is studied in the presence of decoherence using the Barenco et al. approach where random phase fluctuations are attached to 2-qubit gates. The expression for average fidelity is calculated for three cases and it is found to depend on the optimal fidelity and the average of the phase fluctuations in a specific way. It is conjectured to be the form of the average fidelity in the general case. While the cloning network is found to be rather robust, it is nevertheless argued that the scalability of the quantum network implementation is poor by studying the effect of decoherence during the preparation of the initial state of the cloning machine in the 1 ! 2 case and observing that the loss in average fidelity can be large. This affirms the result by Maruyama and Knight, who reached the same conclusion in a slightly different manner.

Glyphosate translocation in herbicide tolerant plants

The objective of this study was to evaluate glyphosate translocation in glyphosate-tolerant weed species (I. nil, T. procumbens and S. latifolia) compared to glyphosate-susceptible species (B. pilosa). The evaluations of 14C-glyphosate absorption and translocation were performed at 6, 12, 36 and 72 hours after treatment (HAT) in I. nil and B. pilosa, and only at 72 HAT in the species T. procumbens and S. latifolia. The plants were collected and fractionated into application leaf, other leaves, stems, and roots. In S. latifolia, approximately 88% of the glyphosate remained in the application leaf and a small amount was translocated to roots at 72 HAT. However, 75% of the herbicide applied on T. procumbens remained in the leaf that had received the treatment, with greater glyphosate translocation to the floral bud. It was concluded that the smaller amount of glyphosate observed in S. latifolia and T. procumbens may partly account for their higher tolerance to glyphosate. However, I. nil tolerance to glyphosate may be associated with other factors such as metabolization, root exudation or compartmentalization, because a large amount of the herbicide reached the roots of this species.

Competition between drought-tolerant upland rice cultivars and weeds under water stress condition

The objective of this study was to evaluate the competitiveness of two cultivars of upland rice drought-tolerant, cultured in coexistence with weed S. verticillata, under conditions of absence and presence of water stress. The experiment was conducted in a greenhouse at the Experimental Station of the Universidade Federal de Tocantins, Gurupi-TO Campus. The experimental design was completely randomized in a factorial 2 x 2 x 4 with four replications. The treatments consisted of two rice cultivars under two water conditions and four densities. At 57 days after emergence, were evaluated in rice cultivars and weed S. verticillata leaf area, dry weight of roots and shoots and total concentration and depth of roots. Was also evaluated in rice cultivars, plant height and number of tillers. Water stress caused a reduction in leaf area, the concentration of roots and vegetative components of dry matter (APDM, and MSR MST) of rice cultivars and Jatoba Catetão and weed S. verticillata. The competition established by the presence of the weed provided reduction of all vegetative components (MSPA, and MSR MST) of cultivars and Jatoba Catetão. It also decreased the number of tillers, the concentration of roots and leaf area. At the highest level of weed competition with rice cultivars, a greater decrease in vegetative components and leaf area of culture, regardless of water conditions.

Glyphosate tolerant volunteer corn control at two development stages

The loss of grains during the harvest of glyphosate tolerant corn may generate volunteer plants, which can interfere in the conventional or glyphosate crop in succession. The current work aim to evaluate the control of the volunteer corn glyphosate tolerant under two weed stages. Aimed to evaluate the control of volunteer glyphosate tolerant corn in two stages of development. There were conducted two experiments with hybrid 2B688 HR (lepidoptera and glyphosate tolerant), the application were at V5 and V8 stage. The experiment was randomized block design with four replicates, using the treatments: haloxyfop at 25, 50 and 62 g ha-1 alone and associated with 2,4-D at 670 g ha-1 or fluroxypyr at 200 g ha-1. The standard was clethodim at 84 g ha-1 with 2,4-D and fluroxypyr at same rates. The applications of haloxyfop and clethodim both isolated or in a mixture with 2,4-D and fluroxypyr at V5 stage showed total control (100%) at 32 and 39 days after the application, except for haloxyfop + 2,4-D (25 + 670 g ha-1) mixture, which did not provided adequate control. At V8 stage, haloxyfop + 2,4-D (50 + 670 g ha-1) and haloxyfop + 2,4-D (62 + 670 g ha-1) mixtures took up to 6 and 10 days or longer to reach adequate to excellent control, when compared to haloxyfop isolated applications in the same doses, respectively. Either isolated clethodim or mixed with 2, 4-D and fluroxypyr did not show adequate control. The treatments showed efficient control on volunteer corn plants at V5 stage, except for haloxyfop + 2, 4-D (25 + 670 g ha-1) mixture. At V8 stage applications, haloxyfop either isolated or mixture with fluroxypyr demonstrated excellent control on every evaluated dose. The mixture with 2, 4-D can reduce haloxyfop efficiency at low doses. Clethodim alone or mixed with 2,4-D or furoxypyr did not provide acceptable level of control.