{"paper":{"title":"Quantum Channel Testing in Average-Case Distance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"quant-ph","authors_text":"Animesh Datta, Gregory Rosenthal, Hugo Aaronson, Sathyawageeswar Subramanian, Tom Gur","submitted_at":"2024-09-19T08:39:10Z","abstract_excerpt":"We study the complexity of testing properties of quantum channels. First, we show that testing identity to any channel $\\mathcal N: \\mathbb C^{d_{\\mathrm{in}} \\times d_{\\mathrm{in}}} \\to \\mathbb C^{d_{\\mathrm{out}} \\times d_{\\mathrm{out}}}$ in diamond norm distance requires $\\Omega(\\sqrt{d_{\\mathrm{in}}} / \\varepsilon)$ queries, even in the strongest algorithmic model that admits ancillae, coherence, and adaptivity. This is due to the worst-case nature of the distance induced by the diamond norm.\n  Motivated by this limitation and other theoretical and practical applications, we introduce an a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.12566","kind":"arxiv","version":3},"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/2409.12566/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"}