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Maps preserving a new version of quantum \(f\)-divergence. (English) Zbl 06841252
Summary: For an arbitrary nonaffine operator convex function defined on the nonnegative real line and satisfying \(f(0)=0\), 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 \(f(0)=0\) and \(\lim_{x\to\infty}f(x)/x=\infty\). 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.

MSC:
47B49 Transformers, preservers (linear operators on spaces of linear operators)
47N50 Applications of operator theory in the physical sciences
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