Abstract
Uhlmann's theorem is a cornerstone of quantum information theory, stating that for any quantum state ρ_AB and any state σ_A, there exists an extension σ_AB of σ_A such that the fidelity between ρ_AB and σ_AB equals the fidelity between their marginals ρ_A and σ_A. This property underpins many results and applications in quantum information science. In this work, we generalize Uhlmann's theorem to a broad class of measured f-divergences, including the measured α-R\'enyi divergences for all α ≥ 0. The well-known Uhlmann's theorem for the fidelity corresponds to the special case α = 1/2. Since most commonly used quantum R\'enyi divergences, including the Petz and sandwiched R\'enyi divergences, cannot satisfy this property (except for degenerate cases). This fundamentally distinguishes measured f-divergences from other quantum divergences and highlights their unique mathematical structure.