{
  "abstract": "A universal framework for the joint measurement of multiple localized observables in quantum field theory satisfying spacetime locality and compositionality is still lacking. We present an approach to the problem that is based on the one hand on the positive formalism, an axiomatic framework, where it is clear from the outset that we satisfy locality and compositionality, while also having a consistent probabilistic interpretation. On the other hand, the approach is based on standard tools from quantum field theory, in particular the path integral and the Schwinger-Keldysh formalism. After an overview of the conceptual foundations we introduce the modulus-square construction as a formalization of the measurement process for the expectation value of an important class of observables including quadratic observables. We show that this construction has many of the desired properties, including positivity, locality, single measurement recovery and compositionality. We introduce a renormalization scheme for the measurement of quadratic observables that also satisfies compositionality, in contrast to previous renormalization schemes. We discuss relativistic causality, confirming that measurements in our scheme are indeed localized in the spacetime regions where the underlying observables have support.",
  "abstract_shown": true,
  "affiliations": [
    "Institute for Quantum Optics and Quantum Information, Boltzmanngasse 3, 1090 Vienna, Austria",
    "Centro de Ciencias Matemáticas, Universidad Nacional Autónoma de México, C.P. 58190, Morelia, Michoacán, Mexico",
    "International Center for Theory of Quantum Technologies, University of Gdańsk, Wita Stwosza 63, 80-308 Gdańsk, Poland"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0,
        1
      ],
      "name": "Robert Oeckl",
      "orcid": "0000-0003-3447-7897"
    },
    {
      "affs": [
        2
      ],
      "name": "Adamantia Zampeli",
      "orcid": "0000-0002-1517-6127"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/21d7x1yax2407.bib",
  "cited_by": 0,
  "doi": "10.22331/q-2026-10-08-2232",
  "fulltext_url": null,
  "id": "21d7x1yax2407",
  "issns": [
    "2521-327X"
  ],
  "landing_url": "https://quantum-journal.org/papers/q-2026-10-08-2232/",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "3107|Quantum Mechanics and Applications"
    ]
  ],
  "openalex": "W4417299609",
  "pdf_url": "https://quantum-journal.org/papers/q-2026-10-08-2232/pdf/",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": "Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften",
  "ris": "https://research.draconitic.com/paper/21d7x1yax2407.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:58Z",
      "native_id": "10.22331/q-2026-10-08-2232",
      "source": "crossref",
      "url": "https://quantum-journal.org/papers/q-2026-10-08-2232/"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3107|Quantum Mechanics and Applications",
      "subfield": "amo"
    }
  ],
  "title": "Towards local and compositional measurements in quantum field theory",
  "title_text": "Towards local and compositional measurements in quantum field theory",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:17:58Z",
  "url": "https://research.draconitic.com/paper/21d7x1yax2407",
  "venue": "Quantum",
  "versions": []
}