Abstract
Uhlmann's theorem states that, for any two quantum states ρ_AB and 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 reduced states ρ_A and σ_A. In this work, we generalize Uhlmann's theorem to α-R\'enyi relative entropies for α ∈ [1/2,∞], a family of divergences that encompasses fidelity, relative entropy, and max-relative entropy corresponding to α=1/2, α=1, and α=∞, respectively.