Abstract
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.
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Acknowledgments
The authors are grateful to the referee of the paper for the particularly careful reading of the manuscript and for making several useful comments. The authors were supported by the “Lendület” Program (LP2012-46/2012) of the Hungarian Academy of Sciences and by the National Research, Development and Innovation Office (Grant No. K115383).
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Gaál, M., Molnár, L. Transformations on density operators and on positive definite operators preserving the quantum Rényi divergence. Period Math Hung 74, 88–107 (2017). https://doi.org/10.1007/s10998-016-0174-8
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DOI: https://doi.org/10.1007/s10998-016-0174-8