{
  "abstract": "We consider a continuous-time quantum walk stroboscopically subjected to projective measurements on two distinct targets with sampling time period $τ$. We construct a general renewal framework for the first-detection amplitude at each target, from which we obtain the associated splitting probabilities. For Hamiltonians with reflection symmetry, we further show that each dual-target first-detection amplitude can be viewed as an interference effect between a pair of single-target first-detection amplitudes. This formulation yields exact expressions for the splitting probabilities and gives special sampling times at which they undergo pointwise discontinuous jumps due to a form of ergodicity breaking associated with dark states. As an illustrative example, we apply the framework to a one-dimensional tight-binding lattice chain with nearest-neighbor hopping, and study the splitting probabilities as functions of the initial position and sampling time. Below a critical sampling time, $0<τ< τ_c$ where $τ_c = 2 π/ ΔE$ with $ΔE$ being the energy bandwidth, the splitting probabilities for large system sizes become equal to $1/2$, independent of the initial position, as long as this position does not coincide with target sites. Above the critical sampling time, $τ\\geq τ_c$, the splitting probabilities deviate from $1/2$ and develop oscillations as a function of initial position. The wavenumber associated with these oscillations is $Q=2\\sin^{-1}(rτ_c/τ)$, where $r$ is a positive integer. We also explore the effects of relative phase and spatial separation between different components of a coherent initial state on the splitting probabilities. Finally, we study how a finite number of measurements modifies the splitting probabilities and broadens the resonances at special sampling times.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.29547",
  "author_total": 4,
  "authors": [
    {
      "name": "Prashant Singh"
    },
    {
      "name": "Sabine Tornow"
    },
    {
      "name": "David A Kessler"
    },
    {
      "name": "Eli Barkai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/br45gnb87b9h8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.29547",
  "fulltext_url": null,
  "id": "br45gnb87b9h8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.29547",
  "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",
      "cond-mat.stat-mech"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W7223210940",
  "pdf_url": "https://arxiv.org/pdf/2610.29547",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/br45gnb87b9h8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:19Z",
      "native_id": "2610.29547",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.29547"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    },
    {
      "field": "physics",
      "origin": "arxiv:cond-mat.stat-mech",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "Splitting Probability in Monitored Quantum Dynamics",
  "title_text": "Splitting Probability in Monitored Quantum Dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:19Z",
  "url": "https://research.draconitic.com/paper/br45gnb87b9h8",
  "venue": "arXiv",
  "versions": []
}