Entanglement in multipartite systems and in particle physics

Since the year 1935, when the cofounders of the quantum theory, Einstein, Podolsky, Rosen and Schrödinger, published their famous works on entanglement, physicists and even philosophers have struggled to understand these novel quantum correlations. In 1964 thanks to John S. Bell it became widely recognized that these correlations cannot be explained through the operation of local common causes. In the following years several experimental investigations started to test the manifestations of entanglement and it became more and more apparent that entanglement can be used for novel applications, e.g. to improve the information capacity or to enable secure cryptography. We want to contribute to a very basic question of the quantum theory: whether a certain state - of multipartite qudit systems or of systems in high energy physics - is entangled or not. This knowedge about a certain state is for multipartite and higher dimensional systems not trival but certainly important and currently under intensive investigations, however, its only the first step. The goal is to characterize probably all entanglement features and its manifestions in experimental setups in a systematic and transparent way, i.e. to learn about the very nature of entanglement itself. For that we have to develop new sets of entanglement measures revealing different aspects of entanglement. The challenge is to find methods to practically compute the proposed measures. By studying Bell inequalities and other manifestations of entanglement in higher dimensional systems and high energy physics we can relate them to the different aspects of entanglement. By studing quantum systems at different energy scales our long term objective is to draw a unified and novel picture about aspects of entanglement and its manifestations and herewith open the possibility for novel applications of quantum theory.

Since the 1935-publications of Einstein, Podolsky, Rosen und Schrödinger about entanglement the researchers and philosophers tried to understand these puzzling quantum correlations. In 1964 John Bell discovered that one cannot understand these quantum correlations via a common local reason. One may summarize it also as: The whole is greater than the sum of its parts. Numerous experiments proved the existence of these quantum correlations in different physical systems and it turned out that they allow for novel applications such as increasing the capacity of information or allow for secure communication (cryptography). In this project we addressed a simple question whether a state of quantum multipartite systems with arbitrary degrees of freedom or a state in High Energy Physics is entangled or not. In particular we were interested to classify and detect different types of entanglement. The answer is not trivial, indeed it was proven that it is never in general possible to find out whether a state is entangled or not in a finite time. Anyway we found general criteria that if they are violated they answer the question. However, if the criteria are not violated, we do not learn something about the entanglement. Fortunately, it turned out that in many cases they are successfully and, moreover, they are experimentally feasible. Herewith, we opened new possibilities for experimenters to question their distinct physical quantum systems. We guess that having now a tool to detect and classify different types of entanglement, we can go over to step two and find out what these new puzzling properties of quantum systems are worse for.