{
  "annotation_id": "966589e4-cf10-4aea-9aee-ec818fbc0656",
  "date_created": "2026-02-17T05:53:20.453000Z",
  "date_modified": "2026-02-17T05:53:20.453000Z",
  "file_hash": "b508005f05ad9a75ed2a8efc14c39e65c064e1bcb6875868a7afd0450b73ae8b",
  "private": false,
  "record": {
    "abstract": "We introduce a category $\\mathsf{qGph}$ of quantum graphs, whose definition is motivated entirely from noncommutative geometry. For all quantum graphs $G$ and $H$ in $\\mathsf{qGph}$, we then construct a quantum graph $[G,H]$ of homomorphisms from $G$ to $H$, making $\\mathsf{qGph}$ a closed symmetric monoidal category. We prove that for all finite graphs $G$ and $H$, the quantum graph $[G,H]$ is nonempty iff the $(G,H)$-homomorphism game has a winning quantum strategy, directly generalizing the classical case.\n  The finite quantum graphs in $\\mathsf{qGph}$ are tracial, real, and self-adjoint, and the morphisms between them are CP morphisms that are adjoint to a unital $*$-homomorphism. We show that Weaver\u0027s two notions of a CP morphism coincide in this context. We also show that every finite reflexive quantum graph is the confusability quantum graph of a quantum channel, answering a question of Daws.",
    "arxiv_id": "2601.09685",
    "authors": [
      "Andre Kornell",
      "Bert Lindenhovius"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.CT",
      "math.MP",
      "math.OA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Quantum graphs of homomorphisms",
    "url": "https://arxiv.org/abs/2601.09685",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "8721b584-9bf9-4047-baf6-1b8cac07ef41",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}