Classification of Quantum Entanglement in Complex Systems and Applications

The quantum phenomenon of entanglement has become one of the fundamental building pieces of modern physics. Not only is it the very basis for a whole field of research, quantum information theory, which yields numerous technological applications (such as quantum computing or quantum cryptography), entanglement also plays important role in other scientific fields throughout the different disciplines, ranging from solid state physics over particle physics to microbiology. Although the importance of entanglement has been widely recognised for several decades, its understanding is still very limited. Only the most simple systems (bipartite systems with two degrees of freedom per particle) are understood quite well, while especially multipartite entanglement still holds several central unanswered questions. One of these questions is the problem of classification of multipartite entanglement, which is the main objective of this research project. Due to its generally very complicated structure, multipartite entanglement can be classified in various ways; e.g. by the involved degrees of freedom, its distillability (i.e. its potential for gaining highly entangled particles out of a higher number of more weakly entangled ones) or by equivalence or inequivalence of entangled states with respect to certain kinds of operations. Apart from these central questions, technical applications as well as deeper and more fundamental questions are of great importance to this project. Technologically, different classes of multipartite entanglement and their respective individual properties hold the capability for unique possibilities of quantum informational application, which due to the lack of understanding and research are based mainly on bipartite entanglement at present. Furthermore, a deeper investigation of entanglement classes (for example in a relativistic setting) offers the possibility to better understand the phenomenon of entanglement itselt, thus contributing to answering the fundamental questions of interpretation of quantum mechanics itself. Since all these questions and problems are strongly dependant on each other, they can only be treated in a meaningful way together. This is the goal of this research project.

The quantum phenomenon of entanglement has become one of the fundamental building pieces of modern physics. Not only is it the very basis for a new field of research, quantum information theory, which yields numerous technological applications (such as quantum computing or quantum cryptography), entanglement also plays an important role in other scientific fields throughout the different disciplines, ranging from solid state physics over particle physics to microbiology. Although the importance of entanglement has been widely recognised for several decades, its understanding is still very limited. Only the simplest systems (bipartite systems with two degrees of freedom per particle) are understood quite well, whereas especially multipartite entanglement still holds several central unanswered questions. One of these questions is the problem of classification of multipartite entanglement and its detection, which is the main objective of this research project. Due to its generally very complicated structure multipartite entanglement can be classified in various ways and the detection depends strongly on the particular system.This project, among other results, was able to provide all the theoretical tools for designing an experiment (performed at the Leiden University) that for the first time proved bipartite bound entanglement for two twisted photons! Bound entanglement is an entanglement that cannot be increased. What can be done with that type of entanglement future research has to uncover.Another experiment investigated four twisted photons. This is already a very complex issue and we provided the theoretical framework to reduce the setup to the relevant quantities that allowed for an experimental investigation. The experiment observed for the first time a particular type of genuine multipartite entanglement known to be very useful to outperform classical devices.