# MathSciDoc: An Archive for Mathematician ∫

#### Functional Analysismathscidoc:1910.43711

Letters in Mathematical Physics, 107, (12), 2267-2290
We describe the structure of all bijective maps on the cone of positive definite operators acting on a finite and at least two-dimensional complex Hilbert space which preserve the quantum 2 -divergence for some 2 . We prove that any such transformation is necessarily implemented by either a unitary or an antiunitary operator. Similar results concerning maps on the cone of positive semidefinite operators as well as on the set of all density operators are also derived.
@inproceedings{hong-yimaps,
title={Maps on positive definite operators preserving the quantum \chi _lpha ^2-divergence},
author={Hong-Yi Chen, Gyrgy Pl Gehr, Chih-Neng Liu, Lajos Molnr, Dniel Virosztek, and Ngai-Ching Wong},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020211503985369240},
booktitle={Letters in Mathematical Physics},
volume={107},
number={12},
pages={2267-2290},
}

Hong-Yi Chen, Gyrgy Pl Gehr, Chih-Neng Liu, Lajos Molnr, Dniel Virosztek, and Ngai-Ching Wong. Maps on positive definite operators preserving the quantum \chi _lpha ^2-divergence. Vol. 107. In Letters in Mathematical Physics. pp.2267-2290. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020211503985369240.