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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.01749 |
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Table of Contents:
- 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 $α$-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 $α=\infty$, respectively.