Transformations on density operators and on positive definite operators preserving the quantum Rényi divergence

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...

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Bibliographic Details
Published in:Periodica mathematica Hungarica 2017-03, Vol.74 (1), p.88-107
Main Authors: Gaál, Marcell, Molnár, Lajos
Format: Article
Language:English
Subjects:
Divergence
Entropy
Mathematics
Mathematics and Statistics
Operators
Transformations
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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.
ISSN:0031-5303
1588-2829
DOI:10.1007/s10998-016-0174-8