{
  "abstract": "We study the persistent quantum and classical memory required for exact heralded storage and retrieval of quantum measurements. Given only black-box access to the measurement channel, we construct an exact compression of the port-based program into an outcome-type record and a quantum register, with total dimension polynomial in the query count. For every universal retrieval processor we prove the bounds $Q+C\\ge\\log_2 n$ and $2Q+C\\ge\\log_2\\bigl((n-1)d^2+1\\bigr)$ on the numbers $Q$ of qubits and $C$ of bits of the program, for $n$-outcome POVMs on $\\mathbb{C}^d$ with $d\\ge2$. For $n\\ge2$, no finite classical memory removes the need for quantum memory: any such processor requires a quantum program of dimension at least $d$, at that dimension its classical alphabet must have at least $n$ symbols, and both minima are attained by a single-query protocol with success $1/d^2$. Combining direct-program compression with a converse from approximate measurement programming gives logarithmic total-memory scaling in $1/(1-p)$ as the uniform success probability $p$ approaches one, at fixed $d,n\\ge2$. At fixed input dimension and target success below one, the optimal total-memory scaling is logarithmic in $n$. We also construct self-contained programs under branch-decomposition access and compare the quantum and classical costs of all constructions, including where the outcome-type record is kept: for POVMs with $n$ nonzero rank-one effects the direct program admits a purely quantum allocation whose register is never larger than that of the minimal-Naimark unitary program and which succeeds more often whenever $n>d$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.36972",
  "author_total": 3,
  "authors": [
    {
      "name": "Filip Turoboś"
    },
    {
      "name": "Ludmiła Marcinkowska"
    },
    {
      "name": "Zbigniew Puchała"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1j8hhe337w892.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.36972",
  "fulltext_url": null,
  "id": "1j8hhe337w892",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.36972",
  "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": "W7224088962",
  "pdf_url": "https://arxiv.org/pdf/2610.36972",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1j8hhe337w892.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:50Z",
      "native_id": "2610.36972",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.36972"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Quantum and Classical Memory for Storage and Retrieval of Quantum Measurements",
  "title_text": "Quantum and Classical Memory for Storage and Retrieval of Quantum Measurements",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:50Z",
  "url": "https://research.draconitic.com/paper/1j8hhe337w892",
  "venue": "arXiv",
  "versions": []
}