{
  "abstract": "I construct a family of time-independent, excitation-preserving spin Hamiltonians realising perfect state transfer from a localised two-excitation state to the symmetric two-excitation Dicke state, for every $N\\ge4$. The Hamiltonian has the physical form $H=\\sum_{i<j}J_{ij}(σ_i^+σ_j^-+σ_j^+σ_i^-)+\\sum_iε_i n_i$ with real couplings, and satisfies $e^{-iHt}|110\\cdots0\\rangle=e^{iϕ}|D_N^{(2)}\\rangle$ at a finite time. An $S_{N-2}$ permutation symmetry on the unoccupied spins reduces the dynamics to a four-dimensional invariant subspace. Requiring $(|ψ_0\\rangle+|D_N^{(2)}\\rangle)/2$ to be a zero eigenvector fixes the on-site energies in closed form and leaves three coupling parameters free. The inverse spectral problem then becomes two polynomial equations in two coupling ratios; eliminating one gives a degree-six reciprocal polynomial, which $z=x+x^{-1}$ converts to a cubic. For the spectral family $(-n,-1,1)$ with odd $n$, factorising the cubic's leading coefficient and evaluating it at $z=-2$ shows that some odd $n$ always produces a real root below $-2$, which a subresultant lifts back to the original system. The existence argument is symbolic and uses no numerical optimisation. Since that coefficient contains no odd powers of $n$, the required $n$ comes with an explicit threshold, not an asymptotic guarantee. I also cost the construction: couplings grow as $N^{1/2}$ and the on-site range as $N^{3/2}$, the transfer time stays within a factor 2.3-3.0 of the Mandelstam-Tamm limit at every size, and the fidelity is sensitive to systematic drift of the spectator-spectator coupling class but tolerant of independent bond disorder, which self-averages. This is a constrained analogue of perfect state transfer: for general real states an unconstrained real symmetric matrix suffices, whereas here the Hamiltonian must have excitation-preserving spin-network form.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09654",
  "author_total": 1,
  "authors": [
    {
      "name": "Soumyojyoti Dutta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/adq5amq4jezdy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09654",
  "fulltext_url": null,
  "id": "adq5amq4jezdy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09654",
  "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",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Information and Cryptography"
    ]
  ],
  "openalex": "W7212128885",
  "pdf_url": "https://arxiv.org/pdf/2609.09654",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/adq5amq4jezdy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.09654",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09654"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Perfect State Transfer from a Localised Two-Excitation State to a Dicke State via Static Spin-Network Hamiltonians",
  "title_text": "Perfect State Transfer from a Localised Two-Excitation State to a Dicke State via Static Spin-Network Hamiltonians",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/adq5amq4jezdy",
  "venue": "arXiv",
  "versions": []
}