{
  "abstract": "This review develops a control-theoretic perspective on measurement-based feedback for continuously monitored open quantum systems, with the main analysis focused on finite-dimensional systems governed by diffusive stochastic master equations. We introduce the relevant state-space, invariant-subspace, and quantum non-demolition structures, interpret quantum filtering as nonlinear observer dynamics, and review open-loop asymptotics, filter stability, state-feedback stabilization, robustness, and reduced-order observer-based control. Particular emphasis is placed on a recurrence--contraction framework, in which Hamiltonian feedback removes non-target invariant obstructions while measurement-induced dynamics provide local exponential contraction. Although the detailed analysis is developed for finite-dimensional diffusive models, the underlying measurement--estimation--feedback architecture is relevant across a broad range of quantum platforms. We further discuss implementation challenges and open problems involving scalable estimation, sampling and delay, adaptation, hybrid and non-Markovian dynamics, practical stability, optimal control, and learning-based design. By organizing these developments around invariance, estimation, recurrence, and contraction, the review provides a tutorial bridge between measurement-based quantum feedback and nonlinear stochastic control.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.06111",
  "author_total": 4,
  "authors": [
    {
      "name": "Weichao Liang"
    },
    {
      "name": "Jing Zhang"
    },
    {
      "name": "Gaoyue Guo"
    },
    {
      "name": "Daoyi Dong"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ae57zar2xcyn8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.06111",
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  "id": "ae57zar2xcyn8",
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  "landing_url": "https://arxiv.org/abs/2609.06111",
  "language": null,
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  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "math-ph"
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      "arxiv",
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  "openalex": "W7212062938",
  "pdf_url": "https://arxiv.org/pdf/2609.06111",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ae57zar2xcyn8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:48Z",
      "native_id": "2609.06111",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.06111"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
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  ],
  "title": "Measurement-Based Feedback of Open Quantum Systems: A Control-Theoretic Review and Tutorial",
  "title_text": "Measurement-Based Feedback of Open Quantum Systems: A Control-Theoretic Review and Tutorial",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/ae57zar2xcyn8",
  "venue": "arXiv",
  "versions": []
}