Measures of quantum information

The Wigner-Yanase-Dyson information measures are prominent examples of the “metric adjusted skew information” constructed from monotone metrics. These measures of quantum information are related to special classes of operator monotone functions and their properties. Our growing knowledge of operator monotone functions has thus become a powerful tool in the study of measures of quantum information. For example, it has given a natural order relation rendering the set of quantum information measures into a lattice.

We give an overview of recent developments in this area with a special regard to the superadditivity conjecture of Wigner and Yanase which, although generally false, still holds true for important classes of states.