On new quantum divergences

Abstract

In this paper, we introduce new quantum divergences of the form where σ and τ are Kubo–Ando operator means such that . More precisely, we show that is a quantum divergence when σ is the weighted Kubo–Ando matrix power mean and τ is the weighted geometric mean. In addition, we construct a new quantum Hellinger-type divergence using the linear approximation of the function . We also study the least-squares problem, the data processing inequality, and in-betweenness property of the matrix means with respect to the quantum Hellinger-type divergence.