From quasi-entropy to skew information

This paper gives an overview about particular quasi-entropies, generalized quantum covariances, quantum Fisher informations, skew-informations and their relations. The point is the dependence on operator monotone functions. It is proven that a skew-information is the Hessian of a quasi-entropy. The skew-information and some inequalities are extended to a von Neumann algebra setting.
Comment: 12 pages