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October 2017 Maps preserving a new version of quantum f-divergence
Marcell Gaál
Banach J. Math. Anal. 11(4): 744-763 (October 2017). DOI: 10.1215/17358787-2017-0015

Abstract

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.

Citation

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Marcell Gaál. "Maps preserving a new version of quantum f-divergence." Banach J. Math. Anal. 11 (4) 744 - 763, October 2017. https://doi.org/10.1215/17358787-2017-0015

Information

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

zbMATH: 06841252
MathSciNet: MR3708527
Digital Object Identifier: 10.1215/17358787-2017-0015

Subjects:
Primary: 47B49
Secondary: 47N50

Rights: Copyright © 2017 Tusi Mathematical Research Group

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Vol.11 • No. 4 • October 2017
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