{
  "abstract": "The linear combination of unitaries (LCU) is a fundamental quantum computing primitive used to embed non-unitary operators into larger systems via ancilla post-selection. In standard LCU implementations, only the zero-state ancilla outcome is retained, while all other measurement branches are discarded as unusable overhead. We study these discarded parts. Every computational-basis outcome of the ancilla projects the system onto a different linear combination of the target unitaries; collecting these outcome states in a matrix gives a factorization $Φ=CX$, where $C$ is determined by the ancilla preparation and the rows of $X$ are the states $U_t|ψ\\rangle$, so that $rank(Φ)\\le K$. Although this holds for any LCU circuit; to make the analysis easier, we use a simplified model circuit with Hadamard gates on the index register and a single rotation qubit in place of the coefficient preparation unitary, in which $C$ is explicit. The structure suggests two complementary applications: (i) in an explicit amplitude-access model, classical low-rank matrix completion can reconstruct the full output (including the target) from a subset of its amplitude entries, while computational basis counts provide intensities and generally require additional phase information for full complex recovery; (ii) treating $C$ as a secret key suggests a candidate quantum trapdoor function, whose security remains informal and depends on the difficulty of structured phase retrieval. The scheme thus turns the \"junk\" ancilla outcomes into a structured resource, possibly opening paths for further applications.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.02986",
  "author_total": 1,
  "authors": [
    {
      "name": "Ammar Daskin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1twd3zh0zpd3b.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.02986",
  "fulltext_url": null,
  "id": "1twd3zh0zpd3b",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.02986",
  "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 Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7160419056",
  "pdf_url": "https://arxiv.org/pdf/2605.02986",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1twd3zh0zpd3b.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2605.02986",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.02986"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Exploiting all ancilla outcomes in linear combinations of unitaries: low-rank recovery and quantum trapdoor functions",
  "title_text": "Exploiting all ancilla outcomes in linear combinations of unitaries: low-rank recovery and quantum trapdoor functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:50Z",
  "url": "https://research.draconitic.com/paper/1twd3zh0zpd3b",
  "venue": "arXiv",
  "versions": []
}