{
  "abstract": "Quantum trajectories capture measurement-conditioned statistics beyond ensemble averages. For finite-dimensional Kraus dynamics, complete-reset and overlap conditions yield a unique invariant law with explicit geometric total-variation contraction. Under finite-reference mixing and quantitative transverse contraction, $C^2$ Kraus perturbations yield two complementary stationary limits: an affine tangent law for local fluctuations and an occupation measure for rare excursions. These limits give leading observable-response formulas, including an excursion contribution at quadratic order; both limits and coefficients depend only on reference Kraus operators and their first derivatives. For Clifford-driven monitored trajectories, group structure verifies the general hypotheses and yields geometric Wasserstein mixing uniformly over intermediate unitaries at fixed dimensions, an equivalence between uniform total-variation ergodicity and a finite nonzero rank-one Kraus product for each fixed unitary, and exact stationary tangent energies. Under partial measurement, tangent dynamics have almost surely finite memory with a sharp exponential tail; every $C^2$ state observable has vanishing first-order stationary response. For weak Hamiltonian perturbations, odd-prime Gross--Wigner mana responds linearly in the perturbation strength $θ$, whereas prime-dimensional stabilizer Rényi entropies scale as $θ^{2α}$, $θ^2\\ln(1/θ)$, and $θ^2$ for fixed $0<α<1$, $α=1$, and $1<α<\\infty$, respectively. Under partial measurement, the leading coefficients are strictly positive precisely for Hamiltonians outside the real span of the measurement projectors; on this quotient, the mana coefficient defines a norm and the order-one logarithmic coefficient an explicit positive-definite quadratic form.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.13470",
  "author_total": 5,
  "authors": [
    {
      "name": "Guocheng Zhen"
    },
    {
      "name": "Xuanrong Yang"
    },
    {
      "name": "Chengkai Zhu"
    },
    {
      "name": "Ranyiliu Chen"
    },
    {
      "name": "Xin Wang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ax9jmg5akcfxm.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.13470",
  "fulltext_url": null,
  "id": "ax9jmg5akcfxm",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.13470",
  "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": "W7164555874",
  "pdf_url": "https://arxiv.org/pdf/2606.13470",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ax9jmg5akcfxm.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T18:21:30Z",
      "native_id": "2606.13470",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.13470"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum Trajectories: Ergodicity, Perturbative Dynamics, and Stationary Response",
  "title_text": "Quantum Trajectories: Ergodicity, Perturbative Dynamics, and Stationary Response",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:33Z",
  "url": "https://research.draconitic.com/paper/ax9jmg5akcfxm",
  "venue": "arXiv",
  "versions": []
}