{"paper":{"title":"Stability theorem of depolarizing channels for the minimal output quantum R\\'enyi entropies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Barry C. Sanders, Eunok Bae, Gilad Gour, Jeonghoon Park, Soojoon Lee","submitted_at":"2015-10-27T09:05:08Z","abstract_excerpt":"We show that the stability theorem of the depolarizing channel holds for the output quantum $p$-R\\'enyi entropy for $p \\ge 2$ or $p=1$, which is an extension of the well known case $p=2$. As an application, we present a protocol in which Bob determines whether Alice prepares a pure quantum state close to a product state. In the protocol, Alice transmits to Bob multiple copies of a pure state through a depolarizing channel, and Bob estimates its output quantum $p$-R\\'enyi entropy. By using our stability theorem, we show that Bob can determine whether her preparation is appropriate."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.07815","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":""},"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"}