For an arbitrary nonaffine operator convex function defined on the nonnegative real line and satisfying , we characterize the bijective maps on the set of all positive definite operators preserving a new version of quantum -divergence. We also determine the structure of all transformations leaving this quantity invariant on quantum states for any strictly convex functions with the properties and . 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.
"Maps preserving a new version of quantum -divergence." Banach J. Math. Anal. 11 (4) 744 - 763, October 2017. https://doi.org/10.1215/17358787-2017-0015