{
  "abstract": "I study how measurement outcomes can remain conditionally dependent over long distances while the underlying state carries only a small internal memory, using one-dimensional rotated cluster states, whose exact matrix product state (MPS) bond dimension is $D=2$ at every rotation angle. Using exact MPS contraction, I compute the conditional mutual information (CMI) of two readout protocols: the entanglement-swapping endpoint CMI decreases from one bit at $θ=0$ to zero at $θ=π/2$, whereas a stationary bulk readout of the locally equivalent conventional cluster state vanishes at both limits. As an exact control, the spin-1 AKLT chain obeys $I_m=(4/9)\\,3^{-m}$, so its CMI length equals its two-point correlation length, for an identifiable but non-generic reason. I then compare learners on the same $N=64$, $θ=0.35$ target. A positive autoregressive GRU learns the computational-basis Born distribution from a few thousand samples, but an exactly computable Bell-basis readout shows that this distribution does not fix the phases. A complex RBM reaches the $N=8$ ground state under an exact objective, while a short generic recurrent variational Monte Carlo pilot is still improving when its runs end. As a positive control, an MPS-induced recurrent model whose hidden state is the bond vector reaches the ground state to near machine precision at $χ=2$, whereas a $χ=1$ control fails. These results show that long CMI does not require a large bond dimension, and that building the small virtual memory into the architecture greatly eases optimization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.39392",
  "author_total": 1,
  "authors": [
    {
      "name": "Ziqi Xu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2r0kd3adphwen.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.39392",
  "fulltext_url": null,
  "id": "2r0kd3adphwen",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.39392",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2610.39392",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2r0kd3adphwen.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:23Z",
      "native_id": "2610.39392",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.39392"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Conditional Information Flow and Neural Representability of One-Dimensional Rotated Cluster States",
  "title_text": "Conditional Information Flow and Neural Representability of One-Dimensional Rotated Cluster States",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:45Z",
  "url": "https://research.draconitic.com/paper/2r0kd3adphwen",
  "venue": "arXiv",
  "versions": []
}