2026-09-08T02:22:04Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:26448 2026-09-05T19:44:08Z ddc:004 open_access

Strict Hierarchy for Quantum Channel Certification to Unitary Chen, Kean Wang, Qisheng Zhang, Zhicheng Quantum algorithms quantum channels quantum certification query complexity entanglement fidelity We consider the problem of quantum channel certification to unitary, where one is given access to an unknown d-dimensional channel ℰ, and wants to test whether ℰ is equal to a target unitary channel or is ε-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: 1) Θ(d/ε²) queries suffice for incoherent access model, matching the lower bound due to Fawzi, Flammarion, Garivier, and Oufkir (COLT 2023). 2) Θ(d/ε) queries suffice for coherent access model, matching the lower bound due to Regev and Schiff (ICALP 2008). 3) Θ(√d/ε) queries suffice for source-code access model, matching the lower bound due to Jeon and Oh (npj Quantum Inf. 2026). This demonstrates a strict hierarchy of complexities for quantum channel certification to unitary across various access models. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Kean Chen and Qisheng Wang and Zhicheng Zhang 2026 Is Part Of LIPIcs, Volume 374, 53rd International Colloquium on Automata, Languages, and Programming (ICALP 2026) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2026.59 urn:nbn:de:0030-drops-264480 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2026.59 eng https://creativecommons.org/licenses/by/4.0/legalcode