{
  "abstract": "We study isotropic random walks on complex projective space in the context of stochastic state-space exploration in open quantum systems. Using results from harmonic analysis on compact rank-one symmetric spaces, first we obtain explicit transition kernels and characterise the evolution of fidelity and geometric observables. Then, we establish the correspondence between the small-step limit and Fubini-Study Brownian motion, and also show that the long-time limit reproduces Haar-random state statistics. At the level of the density matrix, the ensemble evolution formally coincides with an isotropic depolarizing channel at all times. Our main results concern first-passage statistics to high-fidelity target states. In the Brownian limit, we derive a closed-form expression for the mean first-passage time and an explicit spectral representation of the first-passage-time distribution, with decay rates determined by the eigenvalues of the killed Fubini-Study Laplace-Beltrami operator. The resulting asymptotics reveal a strong dependence on target fidelity and Hilbert-space dimension, demonstrating the rapidly increasing difficulty of reaching high-fidelity targets through unbiased isotropic exploration. The model is purely geometric and does not incorporate microscopic Hamiltonians or Lindblad dynamics. Nevertheless, the results suggest that it offers a natural starting point for stochastic models of open quantum systems that incorporate Hamiltonian and dissipative effects, with potential applications to stochastic quantum state preparation and control.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.11438",
  "author_total": 1,
  "authors": [
    {
      "name": "Gyula I. Tóth"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/31ch9pesy8j20.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.11438",
  "fulltext_url": null,
  "id": "31ch9pesy8j20",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.11438",
  "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",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7164323988",
  "pdf_url": "https://arxiv.org/pdf/2606.11438",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/31ch9pesy8j20.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T15:21:24Z",
      "native_id": "2606.11438",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.11438"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Isotropic random walks and Brownian diffusion on complex projective space",
  "title_text": "Isotropic random walks and Brownian diffusion on complex projective space",
  "type": "preprint",
  "updated_at": "2026-11-06T18:21:01Z",
  "url": "https://research.draconitic.com/paper/31ch9pesy8j20",
  "venue": "arXiv",
  "versions": []
}