Novel theoretical tools for quantum many-body systems

The research project lies within the field of Quantum Information, which combines Information Theory with Quantum Physics. This combination allows for important and fascinating possibilities of information processing that do not have a classical counterpart. The enormous effort of many experimental groups led already to prototypes of small quantum information processors. Apart from the applications within Quantum Information Theory (QIT), the concepts and tools developed there, turned out to have also relevant implications in other fields of science. Most of these abstract and practical applications are due to the subtle properties of quantum many-body states. Central is entanglement, which is a quantum correlation between particles, without a classical equivalent. Hence, the characterization, qualification, and quantification of entanglement is at the heart of QIT. In order to build a quantum information processor, capable of processing many qubits, further experimental as well as theoretical research is required. This is why the main aim of the project was to develop and exploit new theoretical tools for the description and investigation of many-body quantum systems. The main findings of the present project can be divided into two parts. First, within abstract entanglement theory, a relevant class of operations, the so-called local operations assisted by classical communication (LOCC) has been intensively investigated. This class plays a central role in entanglement theory, as it constitutes those operations, which can be implemented without consuming entanglement. Prior to the research performed here, only very few LOCC transformation among states describing a quantum many-body system, were known. This is, due to the fact that, these operations are very complex. However, we could show that almost no LOCC transformation is possible among pure states and identified sets of states, which can be converted via LOCC. Furthermore, a complete set of entanglement measures for generic multipartite states have been presented. These results, together with all their consequences, do not only substantially advance the theory of multipartite entanglement in quantum information but also provide novel tools to study many-body correlations, which occur in e.g. condensed-matter systems. Second, new algorithms were identified which can be simulated by an exponentially smaller quantum systems. This compressed quantum computations is of practical relevance since it shows that e.g. quantum phase transitions of a large system can be observed experimentally with current technology. We extended this notion to various other models and evolutions, which are relevant in condensed matter theory. Moreover, we demonstrated that compressed computation can be utilized in quantum metrology. In the course of the START project, 30 papers were published in renowned journals. Due to the relevance of the results, the members of the research group have been invited to numerous conferences to talk about them in addition to many further conference contributions, where the results of the project were presented.