"The proposed project addresses fundamental problems at the mathematical/statistical foundations of quantum information theory, with a special focus on the problem of discriminating quantum states. The main goals are to study asymptotic state discrimination under locality constrained measurements, to explore how criticality of the systems influences the validity of asymptotic state discrimination results, to extend existing binary results to multiple hypotheses, to determine the strong converse exponents for binary state discrimination and classical information transmission through quantum channels, and to investigate the approximate correctability of quantum noise that does not change the distinguishability of states too much. These will be addressed through a systematic study of operator distinguishability measures and their behaviour in the given specific problems.The results of the project are expected to shed light on the role of quantum correlations in state discrimination andthe classical information transmission capacity of quantum channels, and yield a better understanding of the asymptotic behaviour of information quantities in critical quantum systems. These questions are at the forefront of current research in quantum information theory and the results of the project are expected to have a great impact on the field."