Maps on positive definite operators preserving the quantum $\chi_\alpha^2$-divergence
Mathematical Physics
2018-02-16 v1 Functional Analysis
math.MP
Quantum Physics
Abstract
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 -divergence for some . 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.
Cite
@article{arxiv.1701.02523,
title = {Maps on positive definite operators preserving the quantum $\chi_\alpha^2$-divergence},
author = {Hong-Yi Chen and György Pál Gehér and Chih-Neng Liu and Lajos Molnár and Dániel Virosztek and Ngai-Ching Wong},
journal= {arXiv preprint arXiv:1701.02523},
year = {2018}
}