{
  "abstract": "Entangling measurements can reduce the cost of learning many-body correlations. We consider classical shadows in which a fixed unitary on a $k$-qubit region is sandwiched between two layers of random single-qubit Clifford gates, and ask which middle unitary best estimates Pauli strings with full support on the region. Combining symplectic support counting with a constraint from operator-size parity, we prove that within this architecture the minimum squared shadow norm over all Clifford middle unitaries is $C_k^{\\rm opt}=4\\cdot 9^k/(3\\cdot 5^k+3^k-6)$ for odd $k$ and $C_k^{\\rm opt}=4\\cdot 9^k/(3\\cdot 5^k-3^k+2)$ for even $k$. A dual-axis rotation circuit $U_*$ attains this minimum for every $k$. Asymptotically $C_k^{\\rm opt}\\simeq(4/3)\\cdot(9/5)^k$: the exponential base of Wu et al.'s contractive unitary is optimal, and the prefactor improves from $2$ to $4/3$. For $1\\leq k\\leq7$, exact certificates show that $U_*$ is optimal over the entire unitary group $\\mathrm U(2^k)$, and we conjecture that this holds for every $k$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04621",
  "author_total": 4,
  "authors": [
    {
      "name": "Xiaotian Nie"
    },
    {
      "name": "Tao Zhang"
    },
    {
      "name": "Yadong Wu"
    },
    {
      "name": "Linghui Chen"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4618ej7nbr5t2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04621",
  "fulltext_url": null,
  "id": "4618ej7nbr5t2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04621",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7220668486",
  "pdf_url": "https://arxiv.org/pdf/2610.04621",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4618ej7nbr5t2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:22Z",
      "native_id": "2610.04621",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04621"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Exact Clifford Optimality for Two-Sided Locally Randomized Classical Shadows",
  "title_text": "Exact Clifford Optimality for Two-Sided Locally Randomized Classical Shadows",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:44Z",
  "url": "https://research.draconitic.com/paper/4618ej7nbr5t2",
  "venue": "arXiv",
  "versions": []
}