{"paper":{"title":"Strict Hierarchy for Quantum Channel Certification to Unitary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"The query complexity for certifying a quantum channel as a target unitary forms a strict hierarchy across three access models.","cross_cats":["cs.CC","cs.DS"],"primary_cat":"quant-ph","authors_text":"Kean Chen, Qisheng Wang, Zhicheng Zhang","submitted_at":"2026-04-29T17:10:34Z","abstract_excerpt":"We consider the problem of quantum channel certification to unitary, where one is given access to an unknown $d$-dimensional channel $\\mathcal{E}$, and wants to test whether $\\mathcal{E}$ is equal to a target unitary channel or is $\\varepsilon$-far from it in the diamond norm. We present optimal quantum algorithms for this problem, settling the query complexities in three access models with increasing power. Specifically, we show that:\n  (i) $\\Theta(d/\\varepsilon^2)$ queries suffice for incoherent access model, matching the lower bound due to Fawzi, Flammarion, Garivier, and Oufkir (COLT 2023)"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We show that (i) Θ(d/ε²) queries suffice for incoherent access model, matching the lower bound due to Fawzi et al. (COLT 2023); (ii) Θ(d/ε) queries suffice for coherent access model, matching Regev and Schiff (ICALP 2008); (iii) Θ(√d/ε) queries suffice for source-code access model, matching Jeon and Oh (npj Quantum Inf. 2026).","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The analysis assumes the standard diamond norm as the distance measure and that the target is exactly a unitary channel; if the distance measure or the notion of 'unitary' changes, the query bounds may not hold.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Optimal algorithms achieve query complexities Θ(d/ε²) for incoherent access, Θ(d/ε) for coherent access, and Θ(√d/ε) for source-code access in quantum channel certification to unitary, exactly matching prior lower bounds.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The query complexity for certifying a quantum channel as a target unitary forms a strict hierarchy across three access models.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"edd427c87db78298a66a331dccb3d30a12673b86382d3e180393fdd5f39c7d7d"},"source":{"id":"2604.26900","kind":"arxiv","version":1},"verdict":{"id":"62964e80-80c6-4201-b1bb-96511d594593","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T10:31:03.929645Z","strongest_claim":"We show that (i) Θ(d/ε²) queries suffice for incoherent access model, matching the lower bound due to Fawzi et al. (COLT 2023); (ii) Θ(d/ε) queries suffice for coherent access model, matching Regev and Schiff (ICALP 2008); (iii) Θ(√d/ε) queries suffice for source-code access model, matching Jeon and Oh (npj Quantum Inf. 2026).","one_line_summary":"Optimal algorithms achieve query complexities Θ(d/ε²) for incoherent access, Θ(d/ε) for coherent access, and Θ(√d/ε) for source-code access in quantum channel certification to unitary, exactly matching prior lower bounds.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The analysis assumes the standard diamond norm as the distance measure and that the target is exactly a unitary channel; if the distance measure or the notion of 'unitary' changes, the query bounds may not hold.","pith_extraction_headline":"The query complexity for certifying a quantum channel as a target unitary forms a strict hierarchy across three access models."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.26900/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-20T23:38:19.010822Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T19:43:30.492069Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"c4bd3093826f9733927e9b7a600e55e89f0f9cdf70d6e9072c33ad1e2a162724"},"references":{"count":35,"sample":[{"doi":"10.1038/s41467-021-27922-0","year":2022,"title":"Quantum algorithmic measurement","work_id":"ac0e1d48-8bfb-4cd3-b7e5-197848b98828","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1109/focs46700.2020.00070","year":2020,"title":"Entanglement is necessary for optimal quantum property testing","work_id":"1ee40ebe-04ea-44eb-af8a-9c0615f9bb74","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1090/conm/305/05215","year":2002,"title":"Quantum amplitude amplification and estimation","work_id":"1e2e43d5-a734-41b6-a5cc-6e1c0d46b56a","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1145/3406325.3451109","year":2021,"title":"VC dimension and distribution-free sample-based testing","work_id":"addb7223-7f92-4d94-b126-812f3bb274e2","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"10.1145/3313276.3316344","year":2019,"title":"Quantum state certification","work_id":"7d12d5f0-aac2-44b6-988a-55e60c6bd5ed","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":35,"snapshot_sha256":"b055ca02d0b08edf3601e55c0e01f04a077dea6ad0c0ade69f15794f070d83f0","internal_anchors":3},"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"}