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 ρAB and σAB equals the fidelity between their reduced states ρ_A and σ_A. In this work, we generalize Uhlmann's theorem to α-Rényi relative entropies for α \in [\frac{1}{2},\infty], a family of divergences that encompasses fidelity, relative entropy, and max-relative entropy corresponding to α=\frac{1}{2}, α=1, and α=∞, respectively.
