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Maps on positive definite operators preserving the quantum \chi _lpha ^2-divergence

Hong-Yi Chen Gyrgy Pl Gehr Chih-Neng Liu Lajos Molnr Dniel Virosztek Ngai-Ching Wong

Functional Analysis mathscidoc: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.
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@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.
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