{
  "abstract": "We consider a fundamental problem of \\emph{mixedness testing}: Given $n$ copies of an $N$-qubit state $ρ$, determine whether $ρ= \\mathbb{I}_d/d$ or $\\|ρ-\\mathbb{I}_d/d\\|_1 \\geq \\varepsilon$ with high probability, where $d = 2^N$. In particular, we focus on performing this task in the practical setting of single-qubit measurements, where measurements are prepared independently on each qubit. We provide a nearly complete picture of single-qubit mixedness tesing by showing $n = \\tildeΘ\\left(\\sqrt{10}^N/\\varepsilon^2\\right)$. To establish our lower bound, we introduce a measurement-dependent lower bound framework for adaptive single-copy state certification. For the upper bound, we present a randomized Pauli basis measurement protocol, which relies on a new primitive for computationally efficient uniformity testing of correlation-concentrated distributions on the Boolean hypercube. In conjunction, we provide lower and upper bounds for mixedness testing with fixed Pauli measurement protocols.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.18839",
  "author_total": 4,
  "authors": [
    {
      "name": "Jayadev Acharya"
    },
    {
      "name": "Abhilash Dharmavarapu"
    },
    {
      "name": "Yuhan Liu"
    },
    {
      "name": "Nengkun Yu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7n0mxqztb6h8z.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.18839",
  "fulltext_url": null,
  "id": "7n0mxqztb6h8z",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.18839",
  "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",
      "cs.CC"
    ],
    [
      "arxiv",
      "cs.IT"
    ],
    [
      "arxiv",
      "math.IT"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7203949174",
  "pdf_url": "https://arxiv.org/pdf/2608.18839",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7n0mxqztb6h8z.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:56Z",
      "native_id": "2608.18839",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.18839"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.IT",
      "subfield": "general"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Near-Optimal Mixedness Testing with Pauli Measurements",
  "title_text": "Near-Optimal Mixedness Testing with Pauli Measurements",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:25Z",
  "url": "https://research.draconitic.com/paper/7n0mxqztb6h8z",
  "venue": "arXiv",
  "versions": []
}