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: (i) $Θ(d/\varepsilon^2)$ queries suffice for incoherent access model, matching the lower bound due to Fawzi, Flammarion, Garivier, and Oufkir (COLT 2023). (ii) $Θ(d/\varepsilon)$ queries suffice for coherent access model, matching the lower bound due to Regev and Schiff (ICALP 2008). (iii) $Θ(\sqrt{d}/\varepsilon)$ 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.

翻译：我们考虑量子信道酉性认证问题：给定对未知 $d$ 维信道 $\mathcal{E}$ 的访问权限，需检验 $\mathcal{E}$ 是否等于目标酉信道，或在钻石范数意义下与目标是否 $\varepsilon$ 远离。本文针对该问题提出最优量子算法，在三种能力递增的访问模型中确定了查询复杂度。具体而言：(i) 在非相干访问模型中，$Θ(d/\varepsilon^2)$ 次查询即充分，该结果匹配 Fawzi、Flammarion、Garivier 与 Oufkir (COLT 2023) 的下界；(ii) 在相干访问模型中，$Θ(d/\varepsilon)$ 次查询即充分，匹配 Regev 与 Schiff (ICALP 2008) 的下界；(iii) 在源码访问模型中，$Θ(\sqrt{d}/\varepsilon)$ 次查询即充分，匹配 Jeon 与 Oh (npj Quantum Inf. 2026) 的下界。这表明不同访问模型下量子信道酉性认证的复杂度存在严格层次结构。