{
  "$type": "site.standard.document",
  "bskyPostRef": {
    "cid": "bafyreiab7463fypxdj7o2x5j26rweuekqznslrvarjnfijxbqpidt6hmya",
    "uri": "at://did:plc:3fychdutjjusoqeq24ljch6q/app.bsky.feed.post/3mkosgr4xfs62"
  },
  "coverImage": {
    "$type": "blob",
    "ref": {
      "$link": "bafkreiflo6xt7is6b2iafwghkjahlgggocme5jwjsbeuqqwcywuvjhmszm"
    },
    "mimeType": "image/png",
    "size": 24783
  },
  "path": "/abs/2604.26900v1",
  "publishedAt": "2026-04-30T00:00:00.000Z",
  "site": "https://arxiv.org",
  "tags": [
    "Kean Chen",
    "Qisheng Wang",
    "Zhicheng Zhang"
  ],
  "textContent": "**Authors:** Kean Chen, Qisheng Wang, Zhicheng Zhang\n\nWe 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.",
  "title": "Strict Hierarchy for Quantum Channel Certification to Unitary"
}