From Quasi-Entropy to Various Quantum Information Quantities

Abstract

The subject is the applications of the use of quasi-entropy in finite dimensional spaces to many important quantities in quantum information. Operator monotone functions and relative modular operators are used. The origin is the relative entropy, and the $f$-divergence, monotone metrics, covariance and the ${\chi }^2$-divergence are the most important particular cases. The extension of monotone metrics to those with two parameters is a new concept. Monotone metrics are also characterized by their joint convexity property.