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.

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Cited by in corpus (1)

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