{
  "abstract": "A quantum channel is called incompatibility-breaking if it always destroys the incompatibility of quantum measurements. On the other extreme are incompatibility-preserving channels, which never destroy incompatibility. This work studies both types of channels through the mathematical framework of zonotopes and zonoids, an approach that provides a complete characterization of compatibility for dichotomic measurements and is particularly powerful in the qubit setting. Using the language of zonoids, we present necessary and sufficient conditions for when a qubit unital channel is incompatibility-breaking, which are also sufficient for nonunital channels. As one of our main results, we demonstrate the superactivation phenomenon of two incompatibility-breaking qubit channels that are no longer incompatibility-breaking when used in parallel. Translating this result into the task of quantum steering, it says that two copies of a two-qubit Werner state can be steered at noise threshold $1/2$, even though this is impossible using just one copy. For the problem of incompatibility preservation, we prove that a quantum channel with matching input and output dimensions will preserve general incompatibility if and only if it is a unitary transformation. When the output dimension is larger, this result no longer holds, and we offer a conjectured form of a general incompatibility-preserving channel.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.06642",
  "author_total": 2,
  "authors": [
    {
      "name": "Eric Chitambar"
    },
    {
      "name": "Yujie Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/405ed6narrzw0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.06642",
  "fulltext_url": null,
  "id": "405ed6narrzw0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.06642",
  "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": "W7220663073",
  "pdf_url": "https://arxiv.org/pdf/2610.06642",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/405ed6narrzw0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:01Z",
      "native_id": "2610.06642",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.06642"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Destroying and Preserving Measurement Incompatibility over a Quantum Channel",
  "title_text": "Destroying and Preserving Measurement Incompatibility over a Quantum Channel",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:01Z",
  "url": "https://research.draconitic.com/paper/405ed6narrzw0",
  "venue": "arXiv",
  "versions": []
}