During the last decade, quantum entanglement has been intensively studied within quantum information science and has also appeared as a natural goal of recent quantum experiments. Because of that the theoretical background of detecting entanglement has been rapidly developing. However, most of this development concentrated on bipartite or few-party entanglement, while today's experiments typically involve many particles. Thus, as one of the most interesting part of quantum optics and quantum information, I chose to study multi-partite entanglement theory, with a stress on creation and generation of many-particle entanglement. There are two main system types in today's experiments. In some systems all particles are individually accessible, such as trapped ions or photons. In such systems entanglement detection is still a challenge as the number of local measurements is limited. I propose to study efficient methods for detecting entanglement in such systems. In other physical systems, such as cold ensembles of a million atoms, particles are not accessible individually and only collective measurements are possible. To obtain useful information about the quantum state is a challenge. I propose to study entanglement creation and detection also in such systems. The latter topic is naturally connected to the efficient modeling of large quantum systems, since exact modeling is not possible for such system sizes.
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