Banach Journal of Mathematical Analysis

Maps preserving a new version of quantum f-divergence

Marcell Gaál

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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 xf(x)/x=. 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.

Article information

Banach J. Math. Anal., Volume 11, Number 4 (2017), 744-763.

Received: 6 July 2016
Accepted: 23 October 2016
First available in Project Euclid: 22 June 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 47B49: Transformers, preservers (operators on spaces of operators)
Secondary: 47N50: Applications in the physical sciences

preservers positive definite operators density operators quantum states relative entropy


Gaál, Marcell. Maps preserving a new version of quantum $f$ -divergence. Banach J. Math. Anal. 11 (2017), no. 4, 744--763. doi:10.1215/17358787-2017-0015.

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