{
  "id": "2404.16004",
  "version": "v2",
  "published": "2024-04-24T17:35:02.000Z",
  "updated": "2024-11-05T00:55:03.000Z",
  "title": "Channel-State duality with centers",
  "authors": [
    "Simon Langenscheidt",
    "Eugenia Colafranceschi",
    "Daniele Oriti"
  ],
  "categories": [
    "quant-ph",
    "hep-th",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We study extensions of the mappings arising in usual channel-state duality to the case of Hilbert spaces with a direct sum structure. This setting arises in representations of algebras with centers, which are commonly associated with constraints, and it has many physical applications from quantum many-body theory to holography and quantum gravity. We establish that there is a general relationship between non-separability of the state and the isometric properties of the induced channel. We also provide a generalisation of our approach to algebras of trace-class operators on infinite dimensional Hilbert spaces.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2024-11-05T00:55:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "infinite dimensional hilbert spaces",
      "quantum many-body theory",
      "direct sum structure",
      "usual channel-state duality",
      "quantum gravity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}