{
  "abstract": "Diffusion-based quantum state tomography (QST) has shown promising results, but all existing methods implicitly adopt a single parameterization (typically Cholesky) without systematic evaluation. We present the first design space study of density matrix parameterizations for diffusion QST, introducing a geometric framework based on the Jacobian Gram matrix $\\mathbf{J}^\\top\\mathbf{J}$. Our calibration of seven parameterizations at 2- and 3-qubit scales, validated by end-to-end training, reveals that \\emph{geometric conditioning alone does not predict end-to-end performance}: at 3-qubit scale, Hermitian direct ($κ= 2.0\\times$) performs worse than Cholesky ($κ= 27\\times$) at all shot levels---a $13.5\\times$ isotropy advantage that translates into a fidelity \\emph{disadvantage} of up to $+0.51$. The 2-qubit ranking (Hermitian $>$ Bloch) reverses at 3 qubits (Bloch 0.907 vs.\\ Hermitian 0.394). We provide a geometric explanation: unbounded parameterizations suffer projection-induced information loss because the PSD constraint couples diagonal and off-diagonal coordinates in ways the unconstrained model cannot respect, whereas the Bloch representation places the maximally mixed state at the center of the valid region, minimizing projection loss.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.09625",
  "author_total": 1,
  "authors": [
    {
      "name": "Shuangu Chang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3tv4g572y0a6b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.09625",
  "fulltext_url": null,
  "id": "3tv4g572y0a6b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.09625",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7202186812",
  "pdf_url": "https://arxiv.org/pdf/2608.09625",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3tv4g572y0a6b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2608.09625",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.09625"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "A Design Space Study of Density Matrix Parameterizations for Diffusion-Based Quantum State Tomography",
  "title_text": "A Design Space Study of Density Matrix Parameterizations for Diffusion-Based Quantum State Tomography",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/3tv4g572y0a6b",
  "venue": "arXiv",
  "versions": []
}