{"paper":{"title":"Uhlmann's theorem for relative entropies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"David Sutter, Giulia Mazzola, Renato Renner","submitted_at":"2025-02-03T19:00:12Z","abstract_excerpt":"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 $\\alpha$-R\\'enyi 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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.01749","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2502.01749/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}