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 χα2-divergence 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.
- Positive definite operators
- Quantum χ -divergence
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics