Maps on quantum states preserving Bregman and Jensen divergences

Abstract

We describe the structure of the bijective transformations on the set of density operators which preserve the Bregman $f$-divergence for an arbitrary differentiable strictly convex function $f.$ Furthermore, we determine the preservers of the Jensen $f$-divergence in the case when the generating function $f$ belongs to a recently introduced function class called Matrix Entropy Class.

v2: published version

References in corpus (3)

• On the joint convexity of the Bregman divergence of matrices
• A family of monotone quantum relative entropies
• Maps on positive definite matrices preserving Bregman and Jensen divergences

Cited by in corpus (3)

• The metric property of the quantum Jensen-Shannon divergence
• Maps on positive definite operators preserving the quantum ${\chi }_{\alpha }^2$-divergence
• Maps on positive operators preserving Rényi type relative entropies and maximal $f$-divergences