Maps on positive definite operators preserving the quantum χα2 -divergence

Hong-Yi, Chen and Gehér, György and Chih-Neng, Liu and Molnár, Lajos and Virosztek, Dániel (2017) Maps on positive definite operators preserving the quantum χα2 -divergence. LETTERS IN MATHEMATICAL PHYSICS, 107 (12). pp. 2267-2290. ISSN 0377-9017

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Abstract

We describe the structure of all bijective maps on the cone of positive definite operators acting on a finite and at least twodimensional complex Hilbert space which preserve the quantum χ 2 αdivergence for some α ∈ [0,1]. 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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