Maps on positive definite operators preserving the quantum ${\chi }_{\alpha }^2$-divergence

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 ${\chi }_{\alpha }^2$-divergence for some $\alpha \in [0,1]$. 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.

References in corpus (4)

• An elementary proof for the non-bijective version of Wigner's theorem
• Maps on positive definite matrices preserving Bregman and Jensen divergences
• Maps on quantum states preserving Bregman and Jensen divergences
• Quantum $f$-divergence preserving maps on positive semidefinite operators acting on finite dimensional Hilbert spaces

Cited by in corpus (1)

• Tensorization of the strong data processing inequality for quantum chi-square divergences