Uhlmann's theorem for relative entropies
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915458584674304 |
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| author | Mazzola, Giulia Sutter, David Renner, Renato |
| author_facet | Mazzola, Giulia Sutter, David Renner, Renato |
| 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_01749 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uhlmann's theorem for relative entropies Mazzola, Giulia Sutter, David Renner, Renato Quantum Physics 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. |
| title | Uhlmann's theorem for relative entropies |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2502.01749 |