Maps on quantum states preserving Bregman and Jensen divergences

TL;DR

This paper characterizes the structure of bijective transformations on quantum states that preserve Bregman and Jensen divergences, providing insights into their mathematical properties and symmetries.

Contribution

It offers a comprehensive description of the preservers of Bregman and Jensen divergences on quantum states, extending previous results to a broad class of functions.

Findings

Characterization of bijective preservers of Bregman f-divergence.

Identification of preservers of Jensen f-divergence within Matrix Entropy Class.

Mathematical structure of transformations maintaining these 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.