{
  "abstract": "Entangled photons play a crucial role in quantum applications, and determining and characterising their entanglement is vital to using them effectively. High-dimensional entangled states offer richer possibilities, but their additional measurement degrees of freedom make them increasingly demanding to characterise. However, adaptive Bell-test methods based on complex simultaneous perturbation stochastic approximation (CSPSA) have so far focused mainly on qubits. Here we numerically investigate a Bell-inequality-violation-based method for detecting entanglement in unknown quantum states. We extend CSPSA to high-dimensional Bell testing by using the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality for bipartite qudits. The resulting protocol can detect Bell-nonlocal correlations in unknown entangled states, whether pure or mixed, without first reconstructing their density matrix. Using 100 optimisation iterations in each of 100 independent finite-shot runs per number of dimensions d, we demonstrate certified CGLMP violations throughout d=2-8. For isotropic mixed states tested at a visibility of just 0.05 above the standard-Fourier violation threshold, we likewise observe confidence-certified CGLMP violations throughout the range of d studied. We compare this direct stochastic approach with quantum state tomography, the standard method for characterising an unknown state. In the matched benchmark, CSPSA uses fewer measurement configurations per attempt from d=6, whereas tomography requires fewer detected pairs per certified result through d=8. We also derive the phase dependence of the CGLMP parameter and clarify the features of its landscape that govern the adaptive search. Because the measurement-setting cost of each CSPSA iteration is independent of dimension, the method offers a particularly attractive route to the certification of high-dimensional entanglement.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.28235",
  "author_total": 4,
  "authors": [
    {
      "name": "Xu Kang Tan"
    },
    {
      "name": "Jesvita Menezes"
    },
    {
      "name": "Sanjan D. Murthy"
    },
    {
      "name": "Adetunmise C. Dada"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3fk076671kytm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.28235",
  "fulltext_url": null,
  "id": "3fk076671kytm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.28235",
  "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 Information and Cryptography"
    ]
  ],
  "openalex": "W7204811358",
  "pdf_url": "https://arxiv.org/pdf/2608.28235",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3fk076671kytm.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:22Z",
      "native_id": "2608.28235",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.28235"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Direct Adaptive Certification of High-Dimensional Entanglement with Bell Tests",
  "title_text": "Direct Adaptive Certification of High-Dimensional Entanglement with Bell Tests",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:22Z",
  "url": "https://research.draconitic.com/paper/3fk076671kytm",
  "venue": "arXiv",
  "versions": []
}