Aspects of entanglement in multipartite and decaying systems

The study and characterisation of quantum entanglement represents an extended effort within the field of quantum information. This thesis addresses two problems. The first regards entanglement in open systems, where it’s more difficult to define a dichotomic (two outcome) observable due to population loss. The second problem concerns genuine multipartite entanglement, that is entanglement between many particles in states that cannot be separable with respect to any possible bipartition of a system. The first chapter consists of an introduction to the basic elements of quantum mechanics and quantum information theory. We briefly describe a few historical facts about quantum mechanics and the study of entanglement, to help put things into perspective. The second chapter is a detailed discussion of the neutral kaon system. These particles are produced in pairs and are described as a particle-antiparticle system. This system displays some unique properties like the violation of CP-symmetry, and shares some characteristics with other mesons, such as neutral particle oscillation and decay. This makes formulating Bell-type inequalities for them more difficult, but also provides the opportunity for new tests. The third chapter continues with the presentation of an already existent effective formalism for performing Bell tests on neutral kaons. The essence of the formalism is a switch to the Heisenberg picture, transferring the time evolution and dependence on measurement directions to a so-called effective operator. This has many advantages, some of the most important being a proper normalization during population loss (due to decay), an easy application to the case of multiple particles and the fact that it allows one to observe entanglement within the system for a relatively long amount of time. The final part presents a way to simulate neutral kaons with atomic systems, namely with Ytterbium isotopes and discuss what are the differences between these atomic systems and neutral kaons. The second part of the thesis treats the problem of proving genuine multipartite entanglement from separable two-body marginals. For this, an introduction to semidefinite programming is necessary due to the fact that the problem under study can be formulated in terms of this method. We will briefly discuss linear and semidefinite programming as well as the concept of duality and provide some basic examples. The formal description of this problem and previous results are provided in the fifth chapter. Our result shows that, through a cyclic iteration between two SDPs, one obtains states with the desired properties. Using this method we managed to go up to six qubit states for various configurations. From this we can construct higher-dimensional states having the same properties.Die Studium und die Charakterisierung von Verschränkung in Quantensystemen ist ein beständiges Ziel in dem Gebiet der Quantuminformationstheorie. Diese Dissertation widmet sich hauptsächlich zwei Problemen: Einerseits dem Studium von Verschränkung in offenen Quantensystemen, wo die Definition einer dichotomischen Observablen wegen Teilchenverlust im System gewisse Schwierigkeiten bereitet. Andrerseits untersucht es echte Mehrteilchen- Verschränkung, welches Verschränkung in Zuständen beschreibt, welche bezüglich aller möglichen Bipartitionen nicht separabel sind. Das erste Kapitel führt in die grundlegenden Elemente der Quantenmechanik und der Quanteninformationstheorie ein. Um den Kontext darzustellen beschreiben wir kurz die historische Entwicklung der Quantenmechanik und im Spezifischen die des Phänomens Verschränkung. Das zweite Kapitel beinhaltet eine detaillierte Diskussion von neutralen Kaon-Systemen. Die Teilchen entstehen in Prozessen als Paare, und lassen sich als Teilchen-Antiteilchen beschreiben. Zudem zeigen diese Systeme einige Besonderheiten, im speziellen die Verletzung der CP-Symmetrie, und teilt im weiteren einige Merkmale mit anderen Mesonen, wie zum Beispiel die neutrale Teilchen-Oszillation und Teilchenzerfall. All dies macht die Formulierung von Bell-artigen Ungleichen anspruchsvoller, andrerseits bietet sich dadurch die Möglichkeit von neuen Experimenten. Das dritte Kapitel präsentiert den bereits existierenden effektiven Formalismus, um Bell-Experimente mit neutralen Kaonen durchzuführen. Einer der Hauptaugenmerke des Formalismus ist der Wechsel ins Heisenberg-Bild, welches die Zeitentwicklung und die Abhängigkeiten zu den Messrichtungungen in den sogenannten effektiven Operator verschiebt. Dies hat viele Vorteile, wobei als einer der wichtigsten die korrekte Normierung bezüglich Teilchenverlust ist. Weiterhin vereinfacht dies die Anwendung auf Mehrteilchen-Verschränkung und gibt die Möglichkeit einer verlängerten Beobachtungsdauer. Zuletzt wird diskutiert, wie sich neutrale Kaonen durch atomare Systeme, namentlich durch Ytterbium Isotope, simulieren lassen, bevor Unterschiede zwischen diesen atomaren Systemen und neutralen Kaonen erörtert werden. Der zweite Teil der Dissertation untersucht das Problem, echte Mehrteilchen-Verschränkung nur durch separable zwei-Teilchen Marginalien zu zeigen. Wir führen dazu in die Methode der semidefinite Programmierung (SDP) ein, und diskutierern sowohl lineare und semidefinite Programmierung als auch das Konzept der Dualität. Weiterhin geben wir einige einfach Beispiele. Eine detaillierte Darstellung dieses Problems sowie bereits bekannte Herangehensweisen erscheinen im fünften Kapitel. Unser Resultat zeigt, dass eine zyklische Iteration zwischen zwei semidefiniten Programmen einen Zustand findet, welcher echt mehrteilchenverschränkt ist, jedoch separable zwei-Teilchen Marginalien hat. Durch diese Methode finden wir Zustände mit von bis zu sechs qubits, welche diese Eigenschaften haben. Aus diesen können dann wiederum höherdimensionale Zustände gebildet werden, welche auch separable zwei-Teilchen Marginalien aufweisen, jedoch echt mehrteilchen-verschränkt sind

Modeling Gilliland Correlation using Genetic Programming

The distillation process is one of the most important processes in industry, especially petroleum refining. Designing a distillation column assesses numerous challenges to the engineer, being a complex process that is approached in various studies. An important component, directly affecting the efficient operation of the column, is the reflux ratio that is correlated with the number of the theoretical stages, a correlation developed and studied by Gililland. The correlation is used in the case of simplified control models of distillation columns and it is a graphical method. However, in many situations, there is the need for an analytical form that adequately approximates the experimental data. There are in the literature different analytical forms which are used taking into account the desired precision. The present article attempts to address this problem by using the technique of Genetic Programming, a branch of Evolutionary Algorithms that belongs to Artificial Intelligence, a recently developed technique that has recorded successful applications especially in process modeling. Using an evolutionary paradigm and by evolving a population of solutions or subprograms composed of carefully chosen functions and operators, the Genetic Programming technique is capable of finding the program or relation that fits best the available data

Susceptibility of Several Northeastern Conifers to Fusarium circinatum and Strategies for Biocontrol

Producción CientíficaFusarium circinatum, the causal of pine pitch canker disease (PPC), is now considered among the most important pathogens of Pinaceae in the world. Although in Europe PPC is only established in the Iberian Peninsula, the potential endangered areas cover over 10 million hectares under the current host distribution and climatic conditions. It is therefore a priority to test the susceptibility of those species and their provenances, within Central and Northern Europe and find biological control agents (BCAs) against the disease. In this study, the susceptibility of Pinus sylvestris, P. mugo and Picea abies Romanian provenances to F. circinatum was tested using three inoculum doses. In parallel, the potential use of Trichoderma atroviride and Trichoderma viride as BCAs against F. circinatum was also tested. This study has demonstrated, for the first time, the susceptibility of P. mugo to F. circinatum. Likewise, the susceptibility of P. abies was also confirmed. The fact that the Romanian provenance of P. sylvestris has not been susceptible to F. circinatum suggests genetic resistance as a potential tool to manage the disease. This, together with the apparent effectiveness of Trichoderma species as BCAs, seems to indicate that an integrated management of the disease might be feasible.European Cooperation in Science and Technology (COST Action FP1406 PINESTRENGTH)Ministerio de Economía, Industria y Competitividad (projects AGL2012-39912 / AGL2015-69370-R)Portuguese Foundation for Science and Technology (grant SFRH/BPD/122928/2016

Pine Pitch Canker and Insects: Relationships and Implications for Disease Spread in Europe

Producción CientíficaThe fungal pathogen Fusarium circinatum (Nirenberg and O’ Donnell) is the causal agent of pine pitch canker (PPC) disease, which seriously affects conifer species in forests and nurseries worldwide. In Europe, PPC is only established in the Iberian Peninsula; however, it is presumed that its range could expand through the continent in the near future. Infection caused by this fungus requires open wounds on the tree, including physical damage caused by insects. Therefore, a relationship probably occurs between PPC and a wide variety of insects. The aim of this review is to outline the taxonomic and ecological diversity of insect species with high potential association with F. circinatum in Europe and elsewhere. The insects were classified as vectors, carriers and wounding agents according to the association level with the PPC disease. In addition, we discuss the insect-mediated spreading of PPC disease in relation to the different phases of forest stand development, from seeds and seedlings in nurseries to mature stands. Lastly, to improve our predictive capacities and to design appropriate intervention measures and strategies for controlling disease dissemination by insects, variables such as geographic location, time of the year and host species should be considered,European Cooperation in Science and Technology (COST Action FP1406 PINESTRENGTH)Ministerio de Economía, Industria y Competitividad - Fondo Europeo de Desarrollo Regional (project AGL2015-69370-R)Centro de Estudios do Ambiente e do Mar (CESAM) (project UID/AMB/50017/2019)Portuguese Foundation for Science and Technology (projects PTDC/AGR-FOR/2768/2014 , POCI-01-0145-FEDER-016785 , SFRH/BPD/122928/2016)Russian Foundation for Basic Research (grant 17-04-01486)Saint Petersburg State Polytechnical University (project 2019-0420

Pine Pitch Canker and Insects: Regional Risks, Environmental Regulation, and Practical Management Options

Producción CientíficaPine pitch canker (PPC), caused by the pathogenic fungus Fusarium circinatum (Nirenberg and O’ Donnell), is a serious threat to pine forests globally. The recent introduction of the pathogen to Southern Europe and its spread in Mediterranean region is alarming considering the immense ecological and economic importance of pines in the region. Pines in forests and nurseries can be infected, resulting in severe growth losses and mortality. The pathogen is known to spread in plants for planting and in seeds, and results from recent studies have indicated that F. circinatum may also spread through phoretic associations with certain insects. With this review, we aim to expand the current understanding of the risk of insect-mediated spread of PPC in different parts of Europe. Through the joint action of a multinational researcher team, we collate the existing information about the insect species spectrum in different biogeographic conditions and scrutinize the potential of these insects to transmit F. circinatum spores in forests and nurseries. We also discuss the impact of environmental factors and forest management in this context. We present evidence for the existence of a high diversity of insects with potential to weaken pines and disseminate PPC in Europe, including several common beetle species. In many parts of Europe, temperatures are projected to rise, which may promote the activity of several insect species, supporting multivoltinism and thus, further amplifying the risk of insect-mediated dissemination of PPC. Integrated pest management (IPM) solutions that comply with forest management practices need to be developed to reduce this risk. We recommend careful monitoring of insect populations as the basis for successful IPM. Improved understanding of environmental control of the interaction between insects, the pathogen, and host trees is needed in order to support development of bio-rational strategies to safeguard European pine trees and forests against F. circinatum in future.European Cooperation in Science and Technology (COST Action FP1406 PINESTRENGTH)Ministerio de Economía, Industria y Competitividad - Fondo Europeo de Desarrollo Regional (project AGL2015-69370-R)Portuguese Foundation for Science and Technology (contract IF/00471/2013/CP1203/CT0001)Russian Foundation for Basic Research (grant 17-04-01486)Saint Petersburg State Polytechnical University (project 2019-0420