Scalable reconstruction schemes for quantum state tomography

The ability to store and manipulate interacting quantum many-body systems, such as linearly arranged ions in ion traps, photonic implementations, and cold atoms in optical lattices, enhanced rapidly during the last years. By now, the number of controllable particles in such systems has reached sizes for which conventional methods of quantum tomography fail due to both, experiment time and post-processing resources. We discuss applications of recently developed strategies to reconstruct state representations which are fully determined by a small fraction of the informationally complete measurements. Experimentally relevant examples for ion-trap, photonic, and cold-gases setups are presented.