{
  "abstract": "It is well-known that every n-qubit unitary can be decomposed into a product of controlled singlequbit unitaries. We show that the control conditions in such a decomposition naturally define a quasi-process function, an object that originally came up in the study of indefinite causal order. Here quasi-process functions yield a representation of every n-qubit unitary in a canonical form, namely, as a quasi-process function unitary (qPFU). We use this representation to show how quantum nonlocality without entanglement (QNLWE) can be understood in terms of unitaries that encode the trade-off between causal order and locality noted in R. Kunjwal and Ä. Baumeler, Phys. Rev. Lett. 131, 120201 (2023). Specifically, we obtain two sufficient (but not necessary) criteria-mutual exclusivity of control conditions (MECC) and Unambiguity-for a unitary to be a process function unitary (PFU), i.e., it admits a qPFU representation where the quasi-process function is a process function, an object that can model paradox-free classical causal loops. We also show the inequivalence of these criteria, neither implying the other. We then show that the circuit depth of MECC unitaries admits a characterization in terms of clique-partitioning problems on Hamming graphs and use this correspondence to provide bounds on the circuit depth of n-qubit MECC unitaries. Finally, we show how MECC unitaries provide a recipe for constructing a unitary purification of the associated process function, thereby providing a large class of unitary processes of interest in quantum causality. The generality of this causality-inspired representation of unitaries makes it a versatile tool for analyzing the structure of quantum circuits in other domains.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.00579",
  "author_total": 2,
  "authors": [
    {
      "name": "Nasra Daher Ahmed"
    },
    {
      "name": "Ravi Kunjwal"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f6q7vaaf08w04.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.00579",
  "fulltext_url": null,
  "id": "f6q7vaaf08w04",
  "issns": [],
  "landing_url": "https://hal.science/hal-05791425v1",
  "language": "en",
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "quant-ph"
    ],
    [
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      "0.phys"
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      "hal",
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    ],
    [
      "openalex",
      "1702|Quantum Computing Algorithms and Architecture"
    ]
  ],
  "openalex": "W7216419954",
  "pdf_url": "https://hal.science/hal-05791425/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f6q7vaaf08w04.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:53Z",
      "native_id": "hal-05791425",
      "source": "hal",
      "url": "https://hal.science/hal-05791425v1"
    },
    {
      "first_seen": "2026-10-30T12:26:03Z",
      "native_id": "2610.00579",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.00579"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Characterizing unitaries via quasi-process functions",
  "title_text": "Characterizing unitaries via quasi-process functions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:26:03Z",
  "url": "https://research.draconitic.com/paper/f6q7vaaf08w04",
  "venue": "HAL",
  "versions": []
}