Quantum $f$-divergence preserving maps on positive semidefinite operators acting on finite dimensional Hilbert spaces

Abstract

We determine the structure of all bijections on the cone of positive semidefinite operators which preserve the quantum $f$-divergence for an arbitrary strictly convex function $f$ defined on the positive halfline. It turns out that any such transformation is implemented by either a unitary or an antiunitary operator.

arXiv commentv2: some typos corrected v3: improved presentation and some new references v4: accepted manuscript version

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Cited by in corpus (3)

• Geometric approach to quantum statistical inference
• Maps on positive definite operators preserving the quantum ${\chi }_{\alpha }^2$-divergence
• Maps on positive operators preserving Rényi type relative entropies and maximal $f$-divergences