{
  "annotation_id": "fc474098-a153-4e17-b11c-a6da1d39b047",
  "date_created": "2026-03-02T18:02:19.766000Z",
  "date_modified": "2026-03-02T18:02:19.766000Z",
  "file_hash": "e04d69b933cff7300fdfc35e9ce32f9731d1c87f0aabcb9e905f8fcb7b7d6092",
  "private": false,
  "record": {
    "abstract": "A triple of spectra (r^A, r^B, r^{AB}) is said to be admissible if there is a\ndensity operator rho^{AB} with (Spec rho^A, Spec rho^B, Spec rho^{AB})=(r^A,\nr^B, r^{AB}). How can we characterise such triples? It turns out that the\nadmissible spectral triples correspond to Young diagrams (mu, nu, lambda) with\nnonzero Kronecker coefficient [M. Christandl and G. Mitchison, to appear in\nComm. Math. Phys., quant-ph/0409016; A. Klyachko, quant-ph/0409113]. This means\nthat the irreducible representation V_lambda is contained in the tensor product\nof V_mu and V_nu. Here, we show that such triples form a finitely generated\nsemigroup, thereby resolving a conjecture of Klyachko. As a consequence we are\nable to obtain stronger results than in [M. Ch. and G. M. op. cit.] and give a\ncomplete information-theoretic proof of the correspondence between triples of\nspectra and representations. Finally, we show that spectral triples form a\nconvex polytope.",
    "arxiv_id": "quant-ph/0511029",
    "authors": [
      "Matthias Christandl",
      "Aram Harrow",
      "Graeme Mitchison"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s00220-006-0157-3",
    "journal_ref": "Commun. Math. Phys., 270, 575-585 (2007)",
    "title": "On Nonzero Kronecker Coefficients and their Consequences for Spectra",
    "url": "https://arxiv.org/abs/quant-ph/0511029"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "914dd062-8295-49d0-a0f4-d459f3cb1651",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}