{"paper":{"title":"A Linearly Convergent Algorithm for Computing the Petz-Augustin Mean","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT","math.OC"],"primary_cat":"quant-ph","authors_text":"Chun-Neng Chu, Wei-Fu Tseng, Yen-Huan Li","submitted_at":"2025-02-10T12:37:10Z","abstract_excerpt":"We study the computation of the Petz-Augustin mean of order $\\alpha \\in (0,1) \\cup (1,\\infty)$, defined as the minimizer of a weighted sum of $n$ Petz-R\\'enyi divergences of order $\\alpha$ over the set of $d$-by-$d$ quantum states, where the Petz-R\\'enyi divergence is a quantum generalization of the classical R\\'enyi divergence. We propose the first algorithm with a non-asymptotic convergence guarantee for solving this optimization problem. The iterates are guaranteed to converge to the Petz-Augustin mean at a linear rate of \\( O\\left( \\lvert 1 - 1/\\alpha \\rvert^T \\right) \\) with respect to th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2502.06399","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/2502.06399/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"}