{
  "abstract": "We construct a family of 2D-local constant-depth quantum circuits that output states whose entanglement entropy across a specified cut cannot be estimated in quantum polynomial time. As constant-depth quantum circuits can be learned from polynomially many quantum samples, our resulting pseudoentangled states are implicitly public-key and not pseudorandom. This separates pseudoentanglement from pseudorandomness in the shallow-circuit regime: the former is possible, while the latter is not. The construction is based on the quantum intractability of the Dense-Sparse Learning Parity with Noise problem introduced in [DJ25] and uses a bounded-fan-in, bounded-fan-out classical randomized encoding for linear maps $\\mathbf{x} \\mapsto \\mathbf{Mx},$ which could be of independent interest. As applications, we obtain quantum hardness for the problem of learning the entanglement structure (across a fixed cut) of the ground-state of 1D and 2D local Hamiltonians. The 1D Hamiltonian has an inverse polynomial gap, whereas the 2D one has a constant gap. This complements the result of [BZZ24] that showed only factoring-based hardness for the 1D case, though achieving a volume versus area entanglement difference.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.31448",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexandru Gheorghiu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7a1mrym7sjqzt.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.31448",
  "fulltext_url": null,
  "id": "7a1mrym7sjqzt",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.31448",
  "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",
      "cs.CR"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7163012699",
  "pdf_url": "https://arxiv.org/pdf/2605.31448",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7a1mrym7sjqzt.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2605.31448",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.31448"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Pseudoentanglement in constant depth: How trivial states can have non-trivial entanglement structure",
  "title_text": "Pseudoentanglement in constant depth: How trivial states can have non-trivial entanglement structure",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/7a1mrym7sjqzt",
  "venue": "arXiv",
  "versions": []
}