Uhlmann's Theorem for Relative Entropies

Uhlmann's theorem states that, for any two quantum states ρ and σ, there exists an extension σ of σ such that the fidelity between ρ and σ equals the fidelity between their reduced states ρ and σ. In this work, we generalize Uhlmann's theorem to α-Rényi relative entropies for α ϵ [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.