{"paper":{"title":"Construction of channels which in every dimension anti-degrade the depolarizing channel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Shayan Roofeh, Vahid Karimipour","submitted_at":"2024-08-11T09:49:52Z","abstract_excerpt":"We consider the depolarizing channel in $d$ dimension defined as $D_x(\\rho)=(1-x)\\rho+x\\: \\textit{tr}({\\rho}) \\frac{I}{d}$, and explicitly find a quantum channel ${\\cal N}_x$ which anti-degrades this, when $x\\geq\\frac{1}{2}$. This proves that the depolarizing channel $D_x$ has zero capacity when $x\\geq\\frac{1}{2}$. As a corollary, this implies that any quantum channel when contaminated by white noise stronger than this value loses its capacity completely. Although by arguments based on symmetric-extendibiliy of the Choi matrix, it is known that the channel is anti-degradable when $x\\geq \\frac{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.05733","kind":"arxiv","version":5},"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/2408.05733/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"}