{
  "annotation_id": "1efb2dc9-e8a6-4b94-8de8-28f0fabf85c3",
  "date_created": "2026-02-17T05:53:26.432000Z",
  "date_modified": "2026-02-17T05:53:26.432000Z",
  "file_hash": "730fed32e748293c3dde242a3c66ce29eb0e046d93cf7a76c66e18f7c729b897",
  "private": false,
  "record": {
    "abstract": "Consider quantum channels with input dimension $d_1$, output dimension $d_2$ and Kraus rank at most $r$. Any such channel must satisfy the constraint $rd_2\\geq d_1$, and the parameter regime $rd_2=d_1$ is called the boundary regime. In this paper, we show an optimal query lower bound $\\Omega(rd_1d_2/\\varepsilon^2)$ for quantum channel tomography to within diamond norm error $\\varepsilon$ in the away-from-boundary regime $rd_2\\geq 2d_1$, matching the existing upper bound $O(rd_1d_2/\\varepsilon^2)$. In particular, this lower bound fully settles the query complexity for the commonly studied case of equal input and output dimensions $d_1=d_2=d$ with $r\\geq 2$, in sharp contrast to the unitary case $r=1$ where Heisenberg scaling $\\Theta(d^2/\\varepsilon)$ is achievable.",
    "arxiv_id": "2601.10683",
    "authors": [
      "Kean Chen",
      "Zhicheng Zhang",
      "Nengkun Yu"
    ],
    "categories": [
      "quant-ph",
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Optimal lower bound for quantum channel tomography in away-from-boundary regime",
    "url": "https://arxiv.org/abs/2601.10683",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2e1515b9-1236-4d81-8587-f7468ed2aa5c",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}