Maps preserving a new version of quantum f-divergence

Abstract

For an arbitrary nonaffine operator convex function defined on the nonnegative real line and satisfying $f\left(0\right)=0$, we characterize the bijective maps on the set of all positive definite operators preserving a new version of quantum $f$-divergence. We also determine the structure of all transformations leaving this quantity invariant on quantum states for any strictly convex functions with the properties $f\left(0\right)=0$ and ${lim\hspace{0.17em}}_{x\to \infty }f\left(x\right)/x=\infty$. Finally, we derive the corresponding result concerning those transformations on the set of positive semidefinite operators. We emphasize that all the results are obtained for finite-dimensional Hilbert spaces.