{"paper":{"title":"Reliability Functions of Quantum Soft Covering and Privacy Amplification via a Mixed-Order R\\'enyi Divergence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.FA","math.IT"],"primary_cat":"quant-ph","authors_text":"Hongsen Qiu, Shi-Bing Li, Xinyu Zhang","submitted_at":"2026-07-29T15:14:46Z","abstract_excerpt":"In this paper, we introduce a novel mixed-order R\\'enyi divergence and investigate its fundamental properties. Using this divergence, we define a family of mixed-order order-two R\\'enyi mutual information and R\\'enyi conditional entropy. We derive exact reliability functions of quantum soft covering and privacy amplification under the sandwiched R\\'enyi divergence with order $\\alpha\\in[2,\\infty)$. The former is jointly characterized by the sandwiched and mixed-order order-two R\\'enyi mutual information quantities, while the latter is characterized by the corresponding conditional entropies. Th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.27015","kind":"arxiv","version":1},"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/2607.27015/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"}