Entanglement properties of multipartite informationally complete quantum measurements

We analyze tight informationally complete measurements for arbitrarily large multipartite systems and study their configurations of entanglement. We demonstrate that tight measurements cannot be exclusively composed neither of fully separable nor maximally entangled states. We establish an upper bound on the maximal number of fully separable states allowed by tight measurements and investigate the distinguished case, in which every measurement operator carries the same amount of entanglement. Furthermore, we introduce the notion of nested tight measurements, i.e. multipartite tight informationally complete measurements such that every reduction to a certain number of parties induces a lower dimensional tight measurement, proving that they exist for any number of parties and internal levels.