Entanglement analysis of atomic processes and quantum registers

During recent years, quantum information processing and the study of N−qubit quantum systems have attracted a lot of interest, both in theory and experiment. Apart from the promise of performing efficient quantum information protocols, such as quantum key distribution, teleportation or quantum computation, however, these investigations also revealed a great deal of difficulties which still need to be resolved in practise. Quantum information protocols rely on the application of unitary and non–unitary quantum operations that act on a given set of quantum mechanical two-state systems (qubits) to form (entangled) states, in which the information is encoded. The overall system of qubits is often referred to as a quantum register. Today the entanglement in a quantum register is known as the key resource for many protocols of quantum computation and quantum information theory. However, despite the successful demonstration of several protocols, such as teleportation or quantum key distribution, there are still many open questions of how entanglement affects the efficiency of quantum algorithms or how it can be protected against noisy environments. To facilitate the simulation of such N−qubit quantum systems and the analysis of their entanglement properties, we have developed the Feynman program. The program package provides all necessary tools in order to define and to deal with quantum registers, quantum gates and quantum operations. Using an interactive and easily extendible design within the framework of the computer algebra system Maple, the Feynman program is a powerful toolbox not only for teaching the basic and more advanced concepts of quantum information but also for studying their physical realization in the future. To this end, the Feynman program implements a selection of algebraic separability criteria for bipartite and multipartite mixed states as well as the most frequently used entanglement measures from the literature. Additionally, the program supports the work with quantum operations and their associated (Jamiolkowski) dual states. Based on the implementation of several popular decoherence models, we provide tools especially for the quantitative analysis of quantum operations. As an application of the developed tools we further present two case studies in which the entanglement of two atomic processes is investigated. In particular, we have studied the change of the electron-ion spin entanglement in atomic photoionization and the photon-photon polarization entanglement in the two-photon decay of hydrogen. The results show that both processes are, in principle, suitable for the creation and control of entanglement. Apart from process-specific parameters like initial atom polarization, it is mainly the process geometry which offers a simple and effective instrument to adjust the final state entanglement. Finally, for the case of the two-photon decay of hydrogenlike systems, we study the difference between nonlocal quantum correlations, as given by the violation of the Bell inequality and the concurrence as a true entanglement measure.

The status and barriers to the implementation and continuation of the school gardening projects in Germany, Nigeria and the United States of America

In drawing a conclusion for this study, care must be taken in generalizing findings since the population of students and teachers investigated were limited to certain levels in the different schools and countries. This study recognized some complexity of the factors underlying the status of school gardening instruction and activities in Germany, Nigeria and the U.S. as inadequate time for decision-making in the process of gardening, motivation of teachers and students. This was seen as the major impediments that influenced the status of gardening in the three countries. However, these factors were considered to have affected students’ mode of participation in the school gardening projects. This research finding suggests that the promotion and encouragement of students in gardening activities will promote vegetable production and increasing the numbers of practical farmers. Gardening has the potential to create opportunities for learning in an environment where children are able to experience nature first hand and to use the shared experience for communication (Bowker & Tearle, 2007). Therefore, the need for students to be encouraged to participate in gardening programs as the benefit will not only reduce the rate of obesity currently spreading among youths, but will contribute to the improve knowledge on science subjects. To build a network between community, parents and schools, a parent’s community approach should be used as the curriculum. The community approach will tighten the link between schools; community members, parents, teachers and students. This will help facilitate a better gardening projects implementation. Through a close collaboration, teachers and students will be able to identify issues affecting communities and undertake action learning in collaboration with community organizations to assess community needs and plan the implementation strategies as parents are part of the community. The sense of efficacy is a central factor in motivational and learning processes that govern educational improvement, standard and performance on complex tasks of both teachers and students. Dedication and willingness are the major stimulator and achievement of a project. Through a stimulator and provision of incentives and facilities, schools can achieve the best in project development. Teachers and principals should be aware that students are the lever for achieving the set goals in schools. Failure to understand what students need will result in achieving zero result. Therefore, it is advised that schools focus more on how to lure students to work through proper collaboration with the parents and community members. Principals and teachers should identify areas where students need to be corrected, helping them to correct the problem will enable them be committed in the schools’ programs.