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Transformations on density operators and on positive definite operators preserving the quantum Rényi divergence. (English) Zbl 1399.47108
Summary: In a certain sense, we generalize the recently introduced and extensively studied notion called quantum Rényi divergence (also called “sandwiched Rényi relative entropy”) and describe the structures of corresponding symmetries. More precisely, we characterize all transformations on the set of density operators which leave our new general quantity invariant and also determine the structure of all bijective transformations on the cone of positive definite operators which preserve the quantum Rényi divergence.

47B49 Transformers, preservers (linear operators on spaces of linear operators)
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