{"paper":{"title":"Data processing for the sandwiched R\\'enyi divergence: a condition for equality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"quant-ph","authors_text":"Cambyse Rouz\\'e, Felix Leditzky, Nilanjana Datta","submitted_at":"2016-04-07T19:12:05Z","abstract_excerpt":"The $\\alpha$-sandwiched R\\'enyi divergence satisfies the data processing inequality, i.e. monotonicity under quantum operations, for $\\alpha\\geq 1/2$. In this article, we derive a necessary and sufficient algebraic condition for equality in the data processing inequality for the $\\alpha$-sandwiched R\\'enyi divergence for all $\\alpha\\geq 1/2$. For the range $\\alpha\\in [1/2,1)$, our result provides the only condition for equality obtained thus far. To prove our result, we first consider the special case of partial trace, and derive a condition for equality based on the original proof of the data"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.02119","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}