Uhlmann's theorem for relative entropies

Abstract

Uhlmann's theorem states that, for any two quantum states ${\rho }_{AB}$ and ${\sigma }_A$, there exists an extension ${\sigma }_{AB}$ of ${\sigma }_A$ such that the fidelity between ${\rho }_{AB}$ and ${\sigma }_{AB}$ equals the fidelity between their reduced states ${\rho }_A$ and ${\sigma }_A$. In this work, we generalize Uhlmann's theorem to $\alpha$-Rényi relative entropies for $\alpha \in [\frac{1}{2},\infty ]$, a family of divergences that encompasses fidelity, relative entropy, and max-relative entropy corresponding to $\alpha =\frac{1}{2}$, $\alpha =1$, and $\alpha =\infty$, respectively.

25 pages, added Appendix A about the relation between sufficiency and Uhlmann property

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Cited by in corpus (1)

• Uhlmann's theorem for measured divergences